
    [hz                       S SK r S SKrS SK7  S rS rS rS rS rS rS	 r	S
 r
S rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS  r S! r!S" r"S# r#S$ r$S% r%S& r&S' r'S( r(S) r)S* r*S+ r+S, r,S- r-S. r.S/ r/S0r0S0r1/ S1Q/ S2Q/ S3Q/ S4Q/ S5Q/ S6Q/ S7Q/ S8Q/ S9Q/ S:Q/ S;Q/ S<Q/ S=Q/ S>Q/ S?Q/r2/ S@Q/ SAQ/ SBQ/ SCQ/ SDQ/ SEQ/ SFQ/ SGQ/ SHQ/ SIQ/ SJQ/ SKQ/ SLQ/ SMQ/ SNQ/r3/ SOQ/ SPQ/ SQQ/ SRQ/ SSQ/ STQ/ SUQ/ SVQ/ SWQ/ SXQ/ SYQ/ SZQ/ S[Q/ S\Q/ S]Q/r4/ SPQ/ S^Q/ S_Q/ S`Q/ SaQ/ SbQ/ ScQ/ SdQ/ SeQ/ SfQ/ SgQ/ ShQ/ SiQ/ SjQ/ SkQ/r5\Rl                  Rn                  Sl 5       r8g)m    N)*c                  p   S[         l        [        S5      R                  S5      (       d   e[        [        5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        S5      R                  S	5      (       d   e[        [        5      R                  S
5      (       d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S[        5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S 5      (       d   e[        SS!5      S"-  R                  S#5      (       d   e[        S$S%5      S%:X  d   e[        S&S%5      [        * :X  d   e[        S'S%5      [        * :X  d   e[        S%S%5      [        * :X  d   e[        S(S%5      [        * :X  d   e[        S)S%5      [        :X  d   e[        S*S%5      [        :X  d   e[        S+S%5      [        :X  d   e[        S,S%5      [        * :X  d   e[        S*S%5      [        :X  d   e[        S-S%5      [        * :X  d   e[        SS%5      [        :X  d   e[        S&S%5      [        * :X  d   e[        SS%5      [        * :X  d   e[        S'S%5      [        * :X  d   e[        SS%5      [        * :X  d   e[        S.S%5      [        * :X  d   e[        SS%5      [        * :X  d   e[        S%S&5      R                  S/5      (       d   e[        SS&5      R                  S05      (       d   e[        S*S&5      R                  S15      (       d   e[        S2S&5      R                  S35      (       d   e[        S%S5      R                  S45      (       d   e[        S%[        5      R                  S55      (       d   e[        SS!5      S"-  R                  S65      (       d   e[        S%S%5      S:X  d   e[        SS%5      S%:X  d   e[        SS%5      S%:X  d   e[        S*S%5      S%:X  d   e[        S-S%5      S%:X  d   e[        S%S&5      R                  S75      (       d   e[        SS&5      R                  S85      (       d   e[        S*S&5      R                  S85      (       d   e[        S2S&5      R                  S95      (       d   e[        S%S5      R                  S:5      (       d   e[        S%[        5      R                  [        S%S5      5      (       d   e[        SS!5      [        S;5      S<-  -  R                  S=5      (       d   e[        S%S%5      [        :X  d   e[        SS%5      [        :X  d   e[        SS%5      [        :X  d   e[        S*S%5      [        :X  d   e[        S-S%5      [        :X  d   e[        S%S&5      R                  S>5      (       d   e[        SS&5      R                  S?5      (       d   e[        S*S&5      R                  S?5      (       d   e[        S2S&5      R                  S@5      (       d   e[        S%S5      R                  SA5      (       d   e[        S%[        5      R                  SB5      (       d   e[        SS!5      [        S;5      SC-  -  R                  SD5      (       d   e[        S;SES;5       H0  n U [         l        [        SFSG5      R                  SH5      (       a  M0   e   g )IN      g|?g.xӿ  g<{Ya?igܝ?gl)?gfE#7?g܋]s?g?z?   gv~H=^0?y      @        gcQC??gHqgt?g3e?   g)_6gg?   y      @       @y	.?Ks?      ?   g<|H׿y      ?       @      @      @yqČn?/G_m    d(	 順 g\zr?      r         ?      ?gٿg333333gffffffg      @grܿgķ&gķ&?      @g[ay^Fk@ĀE!y&q'ѿ-l8KA?gh?g Ȓ#?gVW?g-rPF?y&5#Ȁ#.
   l- gg2@gMה?gbgȀ?gۊv~i@y}.v}^ME%?yhRv俾D;l   8 g
;?d   g     V@g&S8@z}4.00830632138673963619656140653537080438462342928377020695738635559218797348548092636896796324190271316137982810144874264e-41)mpdpsj0aepij1besseljbesselyinfjbesselimpfbesselkrange)ns    T/var/www/auris/envauris/lib/python3.13/site-packages/mpmath/tests/test_functions2.pytest_besselr+      sY   BFa588())))b699*++++d8;;,----c7::+,,,,a588())))b699)****d8;;-....c7::*++++1Q<??233334?566661R=122221T?455551S>233332a=122222a=122221T?PQQQQ4?344444  !MNNNNAv&**+ABBBB4q   3?sd"""3?sd"""1Q<C44t###4s"""2q>S   4s"""4t###2q>S   2q>cT!!!2q>S   3?sd"""1a=SD   3?sd"""1a=SD   3?sd"""1a=SD   1S>455551S>344442c?344443s566661T?JKKKK1Q<??JKKKKAv&**+ABBBB1Q<11Q<11Q<12a=A2a=A1S>233331S>344442c?455553s899991T?KLLLL1Q<??71Q<((((AvR;!77;;<QRRRR1Q<31Q<31Q<32a=C2a=C1S>344441S>233332c?344443s455551T?OPPPP1Q<??JKKKKAvR*!44889NOOOO2c"tG$''  )h  i  i  	i  i     c                  N   S[         l        [        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S	S5      R                  S
5      (       d   e[        SS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        S	S5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        SSS5      R                  S5      (       d   eg )Nr   r   r   @.=@r
   O@2   gE`ߚc@r   ast,@r   r   g!3|"@Go@Ը.?iQX@g{ƶVc@|B(@g^8U)zj@Z@)r   r   besseljzeror   besselyzero r,   r*   test_bessel_zerosr:   P   s   BFq56666q45555q 56666r! 56666s1  !67777q1  !67777q56666q45555q 56666r! 56666s1  !67777q1  !67777r,   c                     S[         l        [        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S	S5      R                  S
5      (       d   e[        S	S5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        S	S5      R                  S5      (       d   e[	        S	S5      R                  S5      (       d   eg )Nr   r   r   y4?L?rܿr   ypH?ķ&r   ypHϿķ&?r   y98y?fh!+r   yXN*5]{?&=ny4?L?r?ypH?ķ&?ypHϿķ&y98y?fh!+@y"'*-@Ay)r   r   hankel1r   hankel2r9   r,   r*   test_hankelr>   _   s9   BF1S>KLLLL1S>IJJJJ2c?KLLLL3sKLLLL3t RSSSS1S>KLLLL1S>IJJJJ2c?KLLLL3sKLLLL3t KLLLLr,   c                  *   S[         l        [        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   e[	        SS5      R                  S5      (       d   eg )	Nr   r
   r   gb	h?      gVi?g߳g?gg]>?)r   r   struvehr   struvelr9   r,   r*   test_struverC   l   s}    BF1Q<??122224?455551Q<??011114?34444r,   c                      S[         l        [        SSS5      R                  S5      (       d   e[	        SSS5      R                  S5      (       d   eg )Nr   r
   r   r   g/GzH@g$+9,@)r   r   whitmr   whitwr9   r,   r*   test_whittakerrG   s   sE    BF1Q<??011111Q<??01111r,   c                     S[         l        [        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[	        SS5      R                  S	5      (       d   e[	        SS5      R                  S
5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   eg )Nr   r
   r   g`'?r   gSҿr	   gHtá굿g+
UAg_xu¿g=V o?guӿr   gkN:gF0آ?g|[)`?gݣ?)r   r   berr   beikerkeir9   r,   r*   test_kelvinrM   x   s=   BFq8;;-....q8;;.////r!9<<01111q8;;.////r!9<</0000q8;;-....r!9<</0000s1:==12222q8;;.////r!9<<.////s1:==01111r,   c                     S[         l        [        SS5      S:X  d   e[        SSS5      S:X  d   e[	        SSSS5      S:X  d   e[        SSSS5      S:X  d   e[        SSSSS5      S:X  d   e[        SSSSSS5      S:X  d   e[        / / S5      S:X  d   e[        / / S5      R                  [        S5      5      (       d   e[        S// S	5      S:X  d   e[        S
SS[        S5      S-  5      R                  S5      (       d   e[        SSS[        S5      S-  5      R                  S5      (       d   e[        SSSS[        -   S-  5      R                  S5      (       d   eS[         l        [        SS5      n [        SS[        -   S/SS[        S-  /[        S5      S-  [        S-  -   5      R                  U 5      (       d   eS[         l        g )Nr   r   r   r
   r   r   r   r   r   r   r   r
   r   r             g?)r   r   r   r
   r   r   P   Q   g?)r   r   r   r
   y0[Ǒ=?u)"?   z1.2282306665029814734863026z-0.1225033830118305184672133   )r   r   hyp0f1hyp1f1hyp1f2hyp2f1hyp2f2hyp2f3hyperr   expr&   r$   mpcvs    r*   test_hyper_miscrg      s   BF!A;!!Aa=A!Aa?a!Aa?a!Aa!!!!!Aa!A!###Bq>QBr?c"g&&&&!R!!!%eCGBJ/2237777%eCGBJ/2237777%eQqS!G,//0Z[[[[BF)+IJA%!A!AaCyQ!A#699!<<<<BFr,   c                  p   S[         l        [        S5      R                  [        S-  5      (       d   e[        S5      R                  [        S5      S-  S[        [        5      -  -  5      (       d   e[        S5      [        :X  d   e[        S5      [        :X  d   e[        S	5      R                  S
5      (       d   e[        S5      R                  S5      (       d   e[        [        S5      [        5      (       d   e[        [        S5      [        5      (       d   e[        S5      R                  S5      (       d   eS[         l        [        SS5      7n [        SS5      7nS[         l        [        U 5      R                  S5      (       d   e[        U5      R                  [        SS5      5      (       d   e[        U 5      R                  S5      (       d   e[        U5      nUR                  R                  S5      (       d   eUR                  S-  R                  S5      (       d   e[        S5      R                  [        S
S5      5      (       d   e[        S5      R                  [        SS5      5      (       d   e[        S5      R                  [        SS 5      5      (       d   e[        S!5      R                  [        SS"5      5      (       d   e[        S#5      R                  [        S$S%5      5      (       d   e[        S&5      R                  [        S$S'5      5      (       d   e[        [        [         5      5      (       d   e[        [        [         5      5      (       d   e[        [        5      S:X  d   e[        [        [        5      [        5      (       d   e[        [        * 5      S:X  d   e[        S5      [        :X  d   e[        S5      R                  [        S-  5      (       d   e[        S5      R                  [        [        S(5      S-  -  [        S5      S-  -  [        S5      S-  S)[        [        5      -  -  -   5      (       d   e[        S5      S:X  d   e[        S5      S:X  d   e[        [        5      [        S[        5      :X  d   e[        [        * 5      [        :X  d   e[        S5      R                  S*5      (       d   e[        S!5      R                  S+5      (       d   e[        S#5      R                  S,5      (       d   e[        S&5      R                  S-5      (       d   e[        S5      R                  S.5      (       d   e[        S/5      R                  [        S-  5      (       d   e[        S/5      R                  [        S-  5      (       d   e[        [        * 5      R                  S05      (       d   eS[         l        [        S[        -  5      R                  S15      (       d   e[        S[        -  5      R                  S25      (       d   e[        S3[        -  5      R                  S45      (       d   e[        S3[        -  5      R                  S55      (       d   e[        [        5      nUR                  R                  S65      (       d   eUR                  R                  S75      (       d   e[        [        5      nUR                  R                  S85      (       d   eUR                  R                  S95      (       d   eS[         l        g ):Nr   r   r
   r   r   r   r         ?        r   z1.3110287771460599052r   z1.1714200841467698589z0.47103424540873331679   i r   i z7.1427724505817781901z7.1427417367963090109z-1.5707923998261688019z1.0000332138990829170z0.999966786328145474069137@B z7.853952181727432z-1.3110287771460599052r0   z0.22326753950210985451z-0.47434723226254522087r   z0.91119556380496500866z0.63133428324134524388y      @      z-0.63133428324134524388y            @z0.95357894880405122483z0.23093044503746114444            z-0.23093044503746114444r   r[   y*0+?{ >y*0+?{ >?y$9@39Zy$9@39Z?`C+?`C+?z1e-1000000000g@z81.724756270009501831744438120951614673874904182624739673z81.437129808135123030101542922290970050337425479058225712z90.5519067523886233967683646782286965823151896970015484512z85.926192483740483797854383268707108012328213431657645509z80.973089521698042334840454592642137667227167622330325225z9-1.156151296372835303836814390793087600271609993858798016z90.4632848917264710404078033487934663562998345622611263332z91.0637961621753130852473300451583414489944099504180510966)r   r   ellipkr   r   gammasqrtr#   
isinstancer&   ellipefractionrd   realimagisnannan)n1n2rf   s      r*   test_elliptic_integralsr|      s   BF!9<<1#;>>%+q.!DH*56666!9$<3":==01111":==01111fRj#&&&&fRj#&&&&#;>>23333BF
5
 	 B
6&
!	!BBF":==01111":==46NOPPPP":==01111r
A669912222FF5L01111!9<<35MNOOOO":==57PQRRRR$<??379QRSSSS$<??379RSTTTT%=C 8:RSTTTT%=C 8:STUUUU#;!fSk3''''3$<1$<3!9<<1#;>>"s1vax.ta7ta4PR89TTUUUU!9>>$<1#;#a*$$$3$<3$<??GHHHH$<??GHHHH%=HIIII%=HIIII!9<<FGGGG/"%%bd++++/"%%bd++++2#;>>,----BF!B$<??UVVVV!B$<??UVVVV#b&>XYYYY#b&>WXXXXr
A6699OPPPP6699PQQQQr
A6699PQQQQ6699PQQQQBFr,   c                  	   S[         l        [        7n [        [        S5      [        -  -   n[        U 5      R                  S5      (       d   e[        U 5      R                  S5      (       d   e[        U 5      R                  S5      (       d   e[        U 5      R                  S5      (       d   e[        U 5      R                  S5      (       d   e[        U 5      R                  S5      (       d   e[        U 5      R                  S	5      (       d   e[        U 5      R                  S
5      (       d   e[        U 5      R                  S5      (       d   e[        U 5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        US-  5      R                  S5      (       d   e[        US-  5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        U5      R                  S5      (       d   e[        S5      S:X  d   e[        S5      [         * :X  d   e[        [         5      [         :X  d   e[#        [        S5      [$        5      (       d   e[        [         5      R                  [&        S-  5      (       d   e[        [         * 5      R                  [&        * S-  5      (       d   e[        [         5      S:X  d   e[        S5      [         * :X  d   e[#        [        S5      [$        5      (       d   e[        [         5      S:X  d   e[        [         5      [         :X  d   e[        [         * 5      S:X  d   e[        [         * 5      S:X  d   e[        [         5      S:X  d   e[        [         5      S:X  d   e[        [         * 5      S:X  d   e[        [         * 5      S:X  d   e[        S5      S:X  d   e[        [         5      [         :X  d   e[        [         * 5      [         * :X  d   e[        S5      [         * :X  d   e[        [         5      [         :X  d   eg )Nr   r   gQal @g	5gR?gc"?g<b?gsu@gU<b@gosf?gl?g8?g!@y?9q@Z:W^@yrʀK@p,?yoO@'<?yҭo*?@Voy6ʺ?_$&P@yH?UPNl@yذ~?	D'?y -l<p/?5?y$67]yb^IcG @r           r   ffffff?r
   gffffffr   r   )r   r   err   r$   eir   lisicishichifresnelsfresnelcairyaiairybir#   rs   r&   r   )xzs     r*   test_exp_integralsr      s   BF	
A	DGAIAa588'((((a588'((((a588'((((a588())))q699())))q699())))A;>>.////A;>>.////!9<<-....!9<<+,,,,a588>????a588>????a588>????a588@AAAAq699?@@@@q699?@@@@AaC=HIIIIAaC=HIIII!9<<GHHHH!9<<CDDDDa5C<<a5SD==c7c>>bgs####c7::bdsd8;;s1uc7a<<a5SD==bh$$$$#;!#;#3$<13$<1C=CC=CSD>T!!!SD>T!!!q6Q;;s8s??t9q6cT>>s8s??r,   c                  R   S[         l        [        S5      [        * :X  d   e[        [        5      [        :X  d   e[        [        * 5      S:X  d   e[        S5      R	                  S5      (       d   eS[         l        [        S5      n Sn[        U 5      U:X  d   e[        S	5      n S
n[        U 5      U:X  d   e[        SS[        -  -   5      n SnSn[        U R                  5      U:X  a  [        U R                  5      U:X  d   eS[         l        [        S5      R	                  S5      (       d   e[        S5      R	                  S5      (       d   eS[         l        [        S5      R	                  S5      (       d   e[        S5      R	                  S5      (       d   e[        [        S[        SS95      nUR                  R	                  SSS[        -  S9(       d   eUR                  R	                  [        5      (       d   e[        S5      R	                  S5      (       d   e[        S5      R	                  S5      (       d   e[        [        S[        SS95      nUR                  R	                  SSS[        -  S9(       d   eUR                  R	                  [        * 5      (       d   e[        S 5      R	                  S!5      (       d   e[        S"5      nUR                  R	                  S#SS[        -  S9(       d   eUR                  R	                  S$5      (       d   eg )%Nr   r   g       y      4@     Q@y;;IWA2,wDr0   i N  z93.8781962825045010930273870085501819470698476975019e+8681i8z8-6.8852261063076355977108174824557929738368086933303e-90r   z9-3.255138234032069402493850638874410725961401274106e+8681z:-2.1081929993474403520785942429469187647767369645423e+8681y    .      Y@z>1.3077239389562548386e+434288 + 7.6808956999707408158e+434287jz?-1.3077239389562548386e+434288 - 7.6808956999707408158e+434287j              $@y$=KFvhI	@              Y@yt9u9m	@      Fx:^V Texactgn xr[   abs_epsrel_eps             $y$=KFvhI	             Yyt9u9m	   Fx:^V y      $@      $@yl	L,N{@y      $      $@gC_d>gJM!	@)r   r   r   r#   r   strr$   rv   rw   r   r   fmulepsr   )rssresimus        r*   test_eir     s   BFa5SD==c7c>>sd8tf:==KLLLL BF
5	ACAq6Q;;
4ABAq6Q;;	%"Q$,A
EC
FCqvv;##aff+"444BF{_````{`aaaaBFc7::CDDDDd8;;DEEEE
4&'A66992Aqu9MMM6699R===d8;;DEEEEe9<<EFFFF
4$'(A66992Aqu9MMM6699bS>>>f:==EFFFF
7A66990!QsU9KKK6699,----r,   c                     S[         l        [        S5      [        :X  d   e[        [        5      S:X  d   e[        [        * 5      [	        [        * [
        * 5      :X  d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        [        S[        SS	95      R                  S
SS[        -  S9(       d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        [        S[        SS	95      R                  SSS[        -  S9(       d   eg )Nr   r   r   y$=KF?v0Oi?r   yt9u?Wr   Tr   yn x;	»r[   r   r   y$=KF?v0Oir   yt9u?W?r   yn x;	;)
r   r   e1r#   rd   r   r   r   r$   r   r9   r,   r*   test_e1r   .  s   BFa5C<<c7a<<sd8sC4"~%%%c7::HIIIId8;;KLLLLd61D)*--.dnoyz{~y~-d8;;IJJJJe9<<LMMMMd7AT*+../eopz{|z.  A  A  Ar,   c                     S[         l        [        SS5      [        :X  d   e[        SS5      R	                  S[
        -  5      (       d   e[        SS5      R	                  S[        S5      -  S-  5      (       d   e[        SS5      R	                  [        S5      * 5      (       d   e[        SS5      R	                  S5      (       d   e[        SS5      R	                  S5      (       d   e[        S	S5      R	                  S
5      (       d   e[        SS5      R	                  S[        [
        5      -  5      (       d   e[        SS5      S:X  d   e[        SS5      R	                  [
        * 5      (       d   e[        SS5      R	                  S5      (       d   e[        SS5      R	                  S5      (       d   e[        SS	[        -
  5      R	                  S5      (       d   e[        SS5      R	                  S5      (       d   e[        SS5      R	                  S5      (       d   e[        SS5      R	                  S[        S5      -  [        S5      -   5      (       d   e[        SS5      S-  R	                  S5      (       d   e[        S[        5      S:X  d   e[        S[        5      S:X  d   e[        S[        5      S:X  d   e[        SS 5      R	                  S!5      (       d   e[        SS5      R	                  S"5      (       d   e[        SS5      R	                  [        S5      * [        [        -  -
  5      (       d   e[        SS#5      R	                  S$5      (       d   e[        S%S5      R	                  S&5      (       d   e[        SS5      R	                  S'5      (       d   e[        SS5      R	                  S(5      (       d   e[        S)S5      [        :X  d   eg )*Nr   r   r   r   r
   r   r   r   r   UUUUUU?r            @gqq?gW   @gH?       @      @yt|*8c??A`?z1.011e-1000g3X@z1.000000000001r   gɫ|?r	   r      r   gA8?g	@y	@       @y              @y&
J`e? ǅ?yJmx-DT!	rl   g/ư>y>ʞư禜?y*oBu|?      )r   r   expintr#   r   r   rc   r   rr   r$   r   r9   r,   r*   test_expintr   :  sF   BF!A;#!A;>>!A#!C=Ac#hJqL))))!A;>>2b6'""""!A;>>!!A;>>$!A;>>$"c?baj))))"R=A"R=QB#q>T""""*Q""#78888$qsQRRRR&)$''(;<<<<"C(++,EFFFF!A;>>!BrF(3r7*++++2bM& $$%9::::!C=A#c?a&"""!B<??LMMMM!A;>>12222!B<??BqE6"Q$;''''!C=JKKKK'!	****!D>PQQQQ"T?QRRRR$q>S   r,   c                  8   S[         l        [        [        S5      S-  5      R	                  S5      (       d   e[        [        S5      S-  5      R	                  S5      (       d   e[        S5      R	                  S5      (       d   e[        S5      R	                  S5      (       d   e[        S	S
-  5      R	                  [        S-  5      (       d   e[        S	S
-  5      S	S
-  -  R	                  S5      (       d   e[        S5      [        S5      * :X  d   e[        S5      R	                  [        S5      [        [        -  -   5      (       d   eS[         l        [         R                  S5      R	                  S5      (       d   e[         R                  S5      R	                  S5      (       d   e[         R                  S5      R	                  S5      (       d   e[         R                  S5      R	                  S5      (       d   e[         R                  S5      R	                  S5      (       d   e[         R                  S5      R	                  S5      (       d   e[         R                  S5      R	                  S5      (       d   e[         R                  S5      R	                  S5      (       d   e[         R                  S 5      R	                  S!5      (       d   e[         R                  S"5      R	                  S#5      (       d   e[         R                  S5      R	                  S$5      (       d   e[         R                  S5      R	                  S%5      (       d   e[         R                  S5      R	                  S&5      (       d   e[         R                  S5      R	                  S'5      (       d   e[         R                  S5      R	                  S(5      (       d   e[         R                  S5      R	                  S)5      (       d   e[         R                  S5      R	                  S*5      (       d   e[         R                  S5      R	                  S+5      (       d   e[         R                  S 5      R	                  S,5      (       d   e[         R                  S"5      R	                  S-5      (       d   e[         R                  S.5      R	                  S/5      (       d   e[         R                  S05      R	                  S15      (       d   e[         R                  S25      R	                  S35      (       d   e[         R                  S45      R	                  S55      (       d   e[         R                  S65      R	                  S75      (       d   e[         R                  S85      R	                  S95      (       d   e[         R                  S:5      R	                  S;5      (       d   e[         R                  S<5      R	                  S=5      (       d   e[         R                  S>5      R	                  S?5      (       d   e[         R                  S@5      R	                  SA5      (       d   e[         R                  S.5      R	                  SB5      (       d   e[         R                  S05      R	                  SC5      (       d   e[         R                  S25      R	                  SD5      (       d   e[         R                  S45      R	                  SE5      (       d   e[         R                  S65      R	                  SF5      (       d   e[         R                  S85      R	                  SG5      (       d   e[         R                  S:5      R	                  SH5      (       d   e[         R                  S<5      R	                  S=5      (       d   e[         R                  S>5      R	                  S?5      (       d   e[         R                  S@5      R	                  SI5      (       d   eSMSJ jn [        R                  [        R                  5      SK:X  d   eU " [        R                  [        R                  5      [        R                  SL-  5      (       d   eU " [        R                  [        R                  5      [        R                  S-  5      (       d   eU " [        R                  [        R                  5      [        R                  * S-  5      (       d   e[        R                  SK5      SK:X  d   eU " [        R                  S5      S5      (       d   eU " [        R                  S5      S5      (       d   eU " [        R                  S5      S5      (       d   eU " [        R                  S5      S5      (       d   eU " [        R                  S5      S5      (       d   eU " [        R                  S5      S5      (       d   eU " [        R                  S5      S5      (       d   eU " [        R                  S5      S5      (       d   eU " [        R                  S 5      S!5      (       d   eU " [        R                  S"5      S#5      (       d   eU " [        R                  S5      S$5      (       d   eU " [        R                  S5      S%5      (       d   eU " [        R                  S5      S&5      (       d   eU " [        R                  S5      S'5      (       d   eU " [        R                  S5      S(5      (       d   eU " [        R                  S5      S)5      (       d   eU " [        R                  S5      S*5      (       d   eU " [        R                  S5      S+5      (       d   eU " [        R                  S 5      S,5      (       d   eU " [        R                  S"5      S-5      (       d   eU " [        R                  S.5      S/5      (       d   eU " [        R                  S05      S15      (       d   eU " [        R                  S25      S35      (       d   eU " [        R                  S45      S55      (       d   eU " [        R                  S65      S75      (       d   eU " [        R                  S85      S95      (       d   eU " [        R                  S:5      S;5      (       d   eU " [        R                  S<5      S=5      (       d   eU " [        R                  S>5      S?5      (       d   eU " [        R                  S@5      SA5      (       d   eU " [        R                  S.5      SB5      (       d   eU " [        R                  S05      SC5      (       d   eU " [        R                  S25      SD5      (       d   eU " [        R                  S45      SE5      (       d   eU " [        R                  S65      SF5      (       d   eU " [        R                  S85      SG5      (       d   eU " [        R                  S:5      SH5      (       d   eU " [        R                  S<5      S=5      (       d   eU " [        R                  S>5      S?5      (       d   eU " [        R                  S@5      SI5      (       d   eg )NNrk   r   rl   z&0.000000999999999999944444444444446111z -13.2382948930629912435014366276r   z$1.5707963267075846569685111517747537z$-4.87506025174822653785729773959e-11r   r   r
   z!-0.372376123661276688262086695553r	   r   r   r0   gdswy      I@       @yRװђA?y              4@yJmhA(-DT!?y             4@y*mbN9<gAy      I       @yRװђ172@rj   ydsw-DT!	@y      I       yRװђ172y             4y*mbN9<gy             4yJmhA(-DT!y      I@       yRװђAgcll?y$ȥU??ty        JmhAy	g*mbNy$ȥU?tgclly$ȥU?t?y	g*mbNAy       Jmhy$ȥU??t?              I@ydsw-DT!?y             I@yRװђx^%B?r   yJmhA(-DT!	@y      4       y*mbNngAy             IyRװђx^%By             Iydsw-DT!y       @      IyRװђI)y      4@       y*mbN	gr   gJmhAy       @      I@yRװђI)?y        cll?y?t?$ȥU?gJmhy*mbNA	gy?t?$ȥUy       clly?t$ȥUy?t$ȥU?c                 :    [        X-
  5      [        U5      U-  :*  $ )N)abs)r   ytols      r*   r   test_trig_integrals.<locals>.ae  s    13x3q6#:%%r,   r                 ?)g-q=)r   r   r   r&   r   r   r   r$   r   r   fpr#   ninf)r   s    r*   test_trig_integralsr   Z  s
   BFc!fWn  !IJJJJc!fWn  !CDDDDf:==?@@@@f:==?@@@@b#g;>>"Q$r3wKC##$GHHHHb6beVb699RURT\""""BF559<<1222255<??LMMMM55:==BCCCC55=KLLLL55=IJJJJ55:==FGGGG55=IJJJJ55=KLLLL55;>>CDDDD55<??LMMMM559<<-....55<??EFFFF55:==1222255=MNNNN55=GHHHH55:==/000055=GHHHH55=MNNNN55;>>3444455<??EFFFF66#;>>GHHHH66&>JKKKK66#;>>CDDDD66&>NOOOO66&>JKKKK66$<??HIIII66%=HIIII66%=MNNNN66":==0111166%=HIIII66#;>>0111166&>GHHHH66#;>>2333366&>MNNNN66&>GHHHH66$<??2333366%=GHHHH66%=MNNNN66":==0111166%=GHHHH&55=AbeeBGGnbeeBh''''beeBFFmRUU1W%%%%beeBGGnruufQh''''558q==beeBi23333beeElMNNNNbeeCjCDDDDbeeFmLMMMMbeeFmJKKKKbeeCjGHHHHbeeFmJKKKKbeeFmLMMMMbeeDkDEEEEbeeElMNNNNbeeBi.////beeElFGGGGbeeCj23333beeFmNOOOObeeFmHIIIIbeeCj01111beeFmHIIIIbeeFmNOOOObeeDk45555beeElFGGGGbffSkHIIIIbffVnKLLLLbffSkDEEEEbffVnOPPPPbffVnKLLLLbffTlIJJJJbffUmIJJJJbffUmNOOOObffRj12222bffUmIJJJJbffSk12222bffVnHIIIIbffSk34444bffVnNOOOObffVnHIIIIbffTl34444bffUmHIIIIbffUmNOOOObffRj12222bffUmHIIIIr,   c                  f   S[         l        [        S5      S-  R                  S5      (       d   e[	        S5      S-  R                  S5      (       d   e[        S5      SS-  -  R                  S	5      (       d   e[	        S5      SS
-  -  R                  S5      (       d   e[        S5      R                  S5      (       d   e[	        S5      R                  S5      (       d   e[        S5      SS-  -  R                  S5      (       d   e[	        S5      SS-  -  R                  S5      (       d   eg )Nr   r   r   gٿ?i ʚ;gL9)?r   i#  g՘T&"@i#  g!#^6@ig4+Y?gP      Y@      Y@   ya0G@N_;@   yݖƻV?i"	)r   r   r   r   r   r9   r,   r*   	test_airyr     s   BF2Jv!!"455552Ju  !455554LT!%%&:;;;;4LT!%%&;<<<<%=34444%=455558RW$(()VWWWW8RW$(()WXXXXr,   c                     S[         l        Sn [        / S/S5      R                  U 5      (       d   e[        / S/S5      R                  U 5      (       d   e[	        SS5      R                  U 5      (       d   e[	        SS5      R                  U 5      (       d   e[	        SS5      R                  S5      (       d   e[	        SS	5      R                  S
5      (       d   eg )Nr   gj	ך9G!@rO   r   r   r   g    eAz4.9679055380347771271e+27455y            eAz=-2.1222788784457702157e+19410 + 5.0840597555401854116e+19410j)r   r   rb   r   r\   re   s    r*   test_hyper_0f1r     s    BFAUGC ##A&&&&TF3""1%%%%$sq!!!!%""""!C=:;;;;!D>\]]]]r,   c                  v   S[         l        Sn [        S/S/S5      R                  U 5      (       d   e[        S/S/S5      R                  U 5      (       d   e[        S/S/S5      R                  U 5      (       d   e[        S/S/S5      R                  U 5      (       d   e[        S/S/S5      R                  U 5      (       d   e[        S/S/S5      R                  U 5      (       d   e[        S/S	/S5      R                  U 5      (       d   e[        S
/S/S5      R                  U 5      (       d   e[        S
/S	/S5      R                  U 5      (       d   e[	        SSS5      R                  U 5      (       d   e[	        SSS5      R                  U 5      (       d   e[	        SSS5      R                  S5      (       d   e[	        SSS5      S-  R                  S5      (       d   e[	        SSS5      R                  S5      (       d   e[	        S[        SS5      S5      R                  S5      (       d   eg )Nr   g[V?rU   rY   r   yffffff?        r   r         ?              ?        r
   r   g    _Bz!2.1555012157015796988e+4342944809y            _Br   y!xL3\F#r   r   '  iar   y(\?KoQyTO9@#y/@)r   r   rb   r   r]   ru   re   s    r*   test_hyper_1f1r     s    BFA%%%((++++%%(++A....#ws#&&q))))#uS!$$Q''''#wv&))!,,,,#uV$''****%&#&))!,,,,&3%$''****&6(6*--a0000#c#!!!$$$$%C ##A&&&&!AdBCCCC1Quf$(()YZZZZ"a""8,,,,"Xa]=1445cddddr,   c                  >   S[         l        Sn [        SS/S/S5      R                  U 5      (       d   e[        SS/S/S5      R                  U 5      (       d   e[        SS/S	/S5      R                  U 5      (       d   e[        SS/S	/S
5      R                  U 5      (       d   e[        SS/S	/S
5      R                  U 5      (       d   e[        SS/S	/S5      R                  U 5      (       d   e[        SS/S/S5      R                  U 5      (       d   e[        SS/S/S
5      R                  U 5      (       d   eSn [        SS[        -   /S/S5      R                  U 5      (       d   e[        SS[        -   /S	/S5      R                  U 5      (       d   e[        SS[        -   /S	/S5      R                  U 5      (       d   e[        SS[        -   /S/S5      R                  U 5      (       d   eSn [        SS/S/S[        S-  -   5      R                  U 5      (       d   e[        SS/S/S[        S-  -   5      R                  U 5      (       d   e[        SS/S/S[        S-  -   5      R                  U 5      (       d   e[        SS/S/S[        S-  -   5      R                  U 5      (       d   eSn [        SS/S/S5      R                  U 5      (       d   e[        SS/S/S5      R                  U 5      (       d   e[        SS/S/S5      R                  U 5      (       d   eS n [        SS/S/S!5      R                  U 5      (       d   e[        SS/S/S!5      R                  U 5      (       d   e[        SS/S/S!5      R                  U 5      (       d   eg )"Nr   g[$?rU   rV   r
   333333?      ?r   g       @y333333?        r          @        y      ?        yO@z?r(,?y?      rY   r   r   皙?r   r               @        r                 y+xV?;CF )r
   r   r   r   )r   r   g?y?        y}?F"?y      @       @)r   r   rb   r   r$   re   s    r*   test_hyper_2f1r     s   BFA%!c*--a0000%S),,Q////#tseS),,Q////#tseV,//2222&%3%033A6666&%3%-003333#ux-003333&'"VHf588;;;;8A%Q!c*--a0000#d1fuc*--a0000#d1fuf-003333#d1fx033A6666A%QCQqS),,Q////#dQCQqS),,Q////#dTFC!G,//2222&!4&#ac'255a88888A&&#.11!4444#fvhs+..q1111#fvhv.11!44448A&&$/2215555#fvht,//2222#fvht,//2222r,   c                     S[         l        [        SSSS5      R                  S5      (       d   e[        SSSSSS9R                  S5      (       d   e[        SS	S	S5      R                  S
5      (       d   e[        SS	S	SSS9R                  S5      (       d   e[        SS	SS5      S:X  d   e[        SSS	S5      [        :X  d   e[        SSSS5      S:X  d   e[        SSSS5      S:X  d   e[        SSSS5      S:X  d   e[        SSSS5      S:X  d   e[        [        SSSS5      5      (       d   e[        SSSS5      R                  S5      (       d   e[        SSSSSS9R                  SS[        -  -   5      (       d   e[        SSSS5      R                  S5      (       d   e[        SSSSSS9R                  S5      (       d   e[        SS	SS5      S:X  d   e[        SSSS5      [        :X  d   e[        S	S	SS5      S:X  d   e[        SS	SS5      R                  S5      (       d   e[        SS SS5      S:X  d   e[        SSSS5      S:X  d   e[        SSSS5      S:X  d   e[        SSSSSS9S:X  d   e[        SSSS5      [        :X  d   e[        SS SS5      [        :X  d   e[        S!S"S#S5      S:X  d   e[        S!SS	S5      R                  S$5      (       d   e[        SS"S#S5      [        :X  d   e[        SS%S#S5      [        * :X  d   e[        [        [        -  S-  5      n [        SS5      S-   [        [        [        -  S&-  5      -  [        SS5      S-  -  n[        S'S(S)U 5      R                  U5      (       d   e[        S'S(S)U R                  5       5      R                  UR                  5       5      (       d   e[        SS*SS+5      R                  S,5      (       d   e[        SS*SS-5      R                  S.5      (       d   e[        SS*SS5      R                  S/5      (       d   e[        SS*S[        5      R                  S05      (       d   e[        SSS1S25      R                  S35      (       d   e[        S4S"SS25      R                  S55      (       d   e[        SSS1S65      R                  S75      (       d   e[        [        SS5       Vs/ s H$  n[        S8S9S:S;[        [        U-  5      -  5      PM&     sn5      R                  S<5      (       d   e[        [        SS5       Vs/ s H$  n[        S8S9S:S=[        [        U-  5      -  5      PM&     sn5      R                  S>5      (       d   e[        [        SS5       Vs/ s H!  n[        S8S9S:[        [        U-  5      5      PM#     sn5      R                  S?5      (       d   e[        SS@SASB5      R                  SC5      (       d   e[        SSSSD5      R                  SE5      (       d   e[        SSSSF5      R                  SG5      (       d   e[        SSSSH5      R                  SI5      (       d   e[        SSSS5      R                  SJ5      (       d   e[        SSSS5      R                  SK5      (       d   e[        SLSMSNSO5      R                  SPS[        SQ-  SR9(       d   eg s  snf s  snf s  snf )SNr   r
   r   r      T)eliminate_allr   r   "   r	      r   r   r   y      ?      ?y??F)	eliminateg     `?g     @?gx&?r   g%α?g]?r   r   rR   r   g?gr   g      gr      z1/2z1/61/3rO   z0.999gQՂ?z1.001yH?1-.MVgN~?yɸa?>eV?r   z0.99gv;@rY   gV?r   yN?Q{?)r   r   rP   r   r
   ffffff?ylJ@ۢ%@g?yIK@K@J> ygObK@v7?r   g      
g+?gSOfEg)\(?yR=@n>jGy)\(??yQ@1~?r   y[N?Sr?yzѿ-DT!g3A?p   )3   r   )r   gwJgUUj   r   )r   r   r_   r   r#   rx   r$   rc   r   nthroot	conjugatefsumr(   r   )r   wks      r*   test_hyper_2f1_hardr     s   BF!Br!""""!Br!$/2248888!Br!####!Br!$/2248888!Br!"""!Br!###!Da D(((!Aa?a!Aa?a!Aa?a!Aa!!!!!Br:&))(3333!Br:7::8hqj;PQQQQ&"b#&))'2222&"b#7::;PQQQQ"R!###!Abs""""R!!!!!Br!%%%%!Br!!!!!Br!!!!!Aa?a!AaE*a///!Aa?c!!!!Br!###$tD#q((($r"Q""4((((!Dq!S(((!Ca SD(((AbDFA	1aQrT"W%galAo5A%eQ'**1----%eQ[[]366q{{}EEEE$q'*--.ABBBB$q'*--.\]]]]$q"%(()?@@@@$q!$''(VWWWW!Aa""#89999%Qv&))*@AAAA!AaMNNNNU1R[Q[uVT#ac(];[QRUU  WB  C  C  C  CU1R[Q[uVT#ac(];[QRUU  WB  C  C  C  CaL1uVS1X6LMPPQ|}}}}!Ce$''(FGGGG!Aa  !MNNNN!Aa	"%%&RSSSS!Aa  !OPPPP!Aa?OPPPP!Aa56666 #w2556PZ[ehikek5lll RQLs   !+[ <+[%([*c                     [        / SQSS/S5      R                  S5      (       d   e[        / SQ/ SQS5      R                  S5      (       d   e[        / SQS	S
/S5      R                  S5      (       d   e[        / SQ/ SQS
5      R                  S5      (       d   e[        / SQ/ SQS5      R                  S5      (       d   e[        / SQ/ SQS5      R                  S5      (       d   e[        / SQ/ SQS
5      R                  S5      (       d   e[        / SQ/ SQS
5      R                  S5      (       d   e[        / SQSS/S5      [        :X  d   e[        / SQSS/S5      R                  S5      (       d   eg )N)r   r
   r   r   r[   r   gLEy?)r   r
   r   r   )r   rR   r   g_g?      ?r   r   g%<@y@CN?mr)r   r
   r   r   r   )rR   r   r[   	   g?g-?yFo?K:ZI)r   gRQ@gp=
ף@g{Gz@)g@gffffff@g333333@ys?+e)r   r   r   r
   )e   r   g	Y@)rb   r   r#   r9   r,   r*   test_hyper_3f2_etcr   B  sS   #a$''(>????7B'**+ABBBB$q1%(()>????71%(()UVVVVYr*--.DEEEEYq),,-BCCCCYq),,-[\\\\#M!4778deeee!Aq!S(((!Iq),,-BCCCCr,   c                     S[         l        [        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      S:X  d   e[        S	S
S5      S:X  d   e[        S	SS5      [        :X  d   e[        S	SS5      S:X  d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      S:X  d   e[        SSS5      S:X  d   e[        SSS5      R                  S[        S5      -  5      (       d   e[        SS[        5      R                  S5      (       d   e[        SSS 5      S!-  R                  S"5      (       d   e[        S#S$S%5      S&-  R                  S'5      (       d   eg )(Nr   r
   r	   r   g?      g[R֯?r   r   r   ir   r   r   gDo7>#?r   gQ2=?r   gMb?      ?   r   y      ?      ?y            ?r   g      @   rR   g?rY   r[   y      Y@      i@r   yiMؿcf)r   r
   r   xr   y       yk9)r   r   hyperur   r#   rr   r   r9   r,   r*   test_hyper_ur   P  s   BF!Bq>T""""!Du%%%%!Aa=C"Qq>T!!!"Qq>S   "R?a!Aa=56666!Bq>45555!Aa=F####!Af$$$"Qy!Z///#c$""1T"X:....!Ab>3444458$U*../^____5&v-112IJJJJr,   c                     S[         l        [        SS// S5      [        SSS5      :X  d   e[        SSS5      R	                  S5      (       d   e[        SSS5      S:X  d   e[        SSS5      S:X  d   e[        SSS5      R	                  S5      (       d   e[        S	SS
5      R	                  S5      (       d   e[        S	SS5      R	                  S5      (       d   e[        S	SS5      R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        SSSSS9S:X  d   e[        SSSSS9S:X  d   eS H1  n U [         l        [        S
SS5      R	                  S 5      (       a  M1   e   g )!Nr   r   r
   r   r   yehǇ?[2222~r   r   r   r   g     @O@r0   i)g-C6?gd?r   r   gMbP?g\1 ?r   y)`?0?)r   rR   rQ   gWuJIgٍ=,?r   y      ?      ?   zeroprec)r   r0   rW   g;On?z1.006867007239309717945323585695344927904000945829843527398772456281301440034218290443367270629519483 + 1.238277162240704919639384945859073461954721356062919829456053965502443570466701567100438048602352623e-46j)r   r   rb   hyp2f0r   )ds    r*   test_hyper_2f0r   f  s   BF!Ar!q1---!Aa=PQQQQ!Aa=A!Aa=A"R?a    "Qst$$$$"Qr?i(((("Qv!!"89999#d5!$$%:;;;;#d4 ##$TUUUU%5699:NOOOO"Qx-222!Bx-222c3&))  +  @  @  	@  @ r,   c                     S[         l        [        S/SS/S5      [        SSSS5      :X  d   eSu  pn[        XUS5      R	                  S5      (       d   e[        XUS	5      R	                  S
5      (       d   e[        XUS5      R	                  S5      (       d   e[        XUS5      R	                  S5      (       d   e[        XUS5      R	                  S5      (       d   e[        XUS5      R	                  S5      (       d   e[        XUS5      R	                  S5      (       d   e[        XUS5      R	                  S5      (       d   e[        XUS5      R	                  S5      (       d   e[        XUS[
        -  5      R	                  S5      (       d   e[        XUS	[
        -  5      R	                  S5      (       d   e[        XUS[
        -  5      R	                  S5      (       d   e[        XUS[
        -  5      R	                  S5      (       d   e[        XUS[
        -  5      R	                  S5      (       d   e[        XUS[
        -  5      R	                  S5      (       d   e[        XUS[
        -  5      R	                  S5      (       d   e[        XUS[
        -  5      R	                  S 5      (       d   e[        XUS[
        -  5      R	                  S!5      (       d   eg )"Nr   r   r
   r   r   )r   r   rP   r   r   gԢr@r   g߷Ar   guT>*Er   gcQr   ga&j۪xrl   z9.8851796978960318255e+867逖 z1.1505659189516303646e+2746 z1.4672005404314334081e+8685r   z!3.6888217332150976493e+8685889636y9)0i#))Fym5,D>@pJs#AyUClsCy6X̝y1RLy(ҾD$hE{B"hz83.5999042951925965458e+613 + 1.5026014707128947992e+613jz;-8.3208715051623234801e+1939 - 3.6752883490851869429e+1941jz:2.0724195707891484454e+6140 - 1.3276619482724266387e+6141jzG-1.1734497974795488504e+6141851462 + 1.1498106965385471542e+6141851462j)r   r   rb   r^   r   r$   )a1b1b2s      r*   test_hyper_1f2r  |  s   BF!aU1!Aa000!HB""2!!"67777"3""#89999"4 ##$=>>>>"5!$$%>????"6"%%&@AAAA"7#&&'CDDDD"5!$$%BCCCC"5!$$%BCCCC"6"%%&IJJJJ"2a4 ##$STTTT"3q5!$$%STTTT"46"%%&TUUUU"57#&&'^____"6!8$''(`aaaa"719%(()cdddd"57#&&'deeee"57#&&'cdddd"6!8$''(qrrrrr,   c            	         S[         l        [        SS// SQS5      [        SSSSSS5      :X  d   eS	u  pp#n[        XX#US
5      R	                  S5      (       d   e[        XX#US5      R	                  S5      (       d   e[        XX#US5      R	                  S5      (       d   e[        XX#US5      R	                  S5      (       d   e[        XX#US5      R	                  S5      (       d   e[        XX#US5      R	                  S5      (       d   e[        XX#US5      R	                  S5      (       d   e[        XX#US5      R	                  S5      (       d   e[        XX#US
[
        -  5      R	                  S5      (       d   e[        XX#US[
        -  5      R	                  S5      (       d   e[        XX#US[
        -  5      R	                  S5      (       d   e[        XX#US[
        -  5      R	                  S5      (       d   e[        XX#US[
        -  5      R	                  S5      (       d   e[        XX#US[
        -  5      R	                  S 5      (       d   e[        XX#US[
        -  5      R	                  S!5      (       d   e[        XX#US[
        -  5      R	                  S"5      (       d   e[        XX#US[
        -  5      R	                  S#5      (       d   eg )$Nr   r   r
   )r   r   r   rR   r   r   r   )r   rP   r   r
   r   r   gJo!m`@r   gb3lKEr   g)&uLQr   g>dxrl   z2.0291718386574980641e865r   z7.7639836665710030977e2742r   z3.2537462584071268759e8681r   z!1.2966030542911614163e+8685889627y*52x!1*r   y V2@(\;-@y.]9ʖC5:4 ly]!2̣!Z3Ly徰gKV7Wgz87.4859161049322370311e+610 - 2.8467477015940090189e+610jz;-1.7477645579418800826e+1938 - 1.7606522995808116405e+1938jz;-1.6932731942958401784e+6137 - 2.4521909113114629368e+6137jzG-2.0988815677627225449e+6141851451 + 5.7708223542739208681e+6141851452j)r   r   rb   ra   r   r$   )r  a2r  r  b3s        r*   test_hyper_2f3r    s   BF!Awq!VAa!Aa%88882NB""b$''(=>>>>"b&))*BCCCC"b'**+CDDDD"b(++,EFFFF"b'**+FGGGG"b'**+GHHHH"b'**+GHHHH"b(++,OPPPP"bA&))*YZZZZ"bQ'**+YZZZZ"ba(++,Z[[[["bq),,-deeee"b*--.fgggg"b+../ijjjj"bq),,-jkkkk"bq),,-jkkkk"b*--.wxxxxr,   c                     S[         l        [        SS/SS/S5      [        SSSSS5      :X  d   eSu  pp#[        XX#S5      R	                  S	5      (       d   e[        XX#S
5      R	                  S5      (       d   e[        XX#S5      R	                  S5      (       d   e[        XX#S5      R	                  S5      (       d   eg )Nr   r   r
   r   r   r   )r   r   rU   r   r   g(wVbAr   z1.2012553712966636711e+4358igir   z+1.1148680024303263661e+43429448190325182840)r   r   rb   r`   r   )r  r  r  r  s       r*   test_hyper_2f2r
    s    BF!A!uQ6!Aa!#4444&KB""b!$$%9::::"e$''(EFFFF"f%(()@AAAA"f%(()VWWWWr,   c                     S[         l        [        SSSS5      R                  S5      (       d   e[        SSSS5      S	:X  d   e[        S
SSS5      R                  S5      (       d   e[        SSSS5      R                  S5      (       d   e[        SSSS5      R                  S5      (       d   e[	        SS5      S:X  d   e[	        SS5      R                  S5      (       d   e[	        SS5      S:X  d   e[	        SS5      S:X  d   e[	        SS5      S:X  d   e[	        SS5      S:X  d   e[	        SS5      S:X  d   e[	        SS5      S:X  d   e[	        SS
5      R                  S5      (       d   e[	        [
        [
        * 5      R                  S5      (       d   e[        SS5      S:X  d   e[        SS5      S:X  d   e[	        SS5      [        :X  d   e[	        SS5      [        * :X  d   e[	        S S5      [        [        [        5      :X  d   e[	        S!S5      [        [        * [        * 5      :X  d   e[        SSS5      R                  S"5      (       d   e[        SS[
        -   S5      R                  S#5      (       d   eg )$Nr   r   r
   r   r   g¹ @r   r   g     %@r   g?r   gVj+\r   r   g{GzĿr   r   g     LA@r   r   iW r   gZb`B?r[   g   `{}@y@/#,?rR   r   r         @y      @      ?y      @      ?g      yUUUUUU?UUUUUU@)r   r   jacobir   legendrer$   chebyuchebytr#   rd   laguerrer9   r,   r*   test_orthpolyr    se   BF"Qq  ----!Aa(((#d1Q""#9::::"aA!!%((((!Ra ##H----Aq>V###C?45555Br?aAb>QAq>QAr?b   Aq>QAr?b   Ac?o....Aqb>KLLLL!A;!!A;"Cs"""Ct###F2#c#,...F2#sdC4.000Ar1  ((((AqsC ##$RSSSSr,   c                  p   S[         l        [        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      S:X  d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S	5      (       d   e[        SS5      R                  S
5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      S:X  d   e[        S	S	5      R                  S5      (       d   e[        SS	5      R                  S5      (       d   e[        S
S	5      R                  S5      (       d   e[        SS	5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S S5      R                  S!5      (       d   e[        S S5      R                  S"5      (       d   e[        S S5      R                  S#S[        S$9(       d   e[        S S5      R                  S%5      (       d   e[        S S5      R                  S&S[        S$9(       d   e[        S S5      R                  S'S[        S$9(       d   e[        S(S[
        -
  5      R                  S)5      (       d   eg )*Nr   r   r   r   r   gkﴑ[?r   r
   r   r   r   ge?r   i  r   i  gj!i(?r	   gb7s[?y              @y           jAy             y          jr   l   d/C'%ld/C'%r   y        M9;Dr   y       M9;g      #y:fTȾQk>y:fTȾQkgyQrd;r   z1.3106082028470671626e4355yRd]Rd]yRd]Rd];r   y@o׿a)r   r   hermiter   r   r$   r9   r,   r*   test_hermiter    sN   BF2q>S!!!!2q>344441a=A1a=A1a=B1a=A1a=A1b>R    1b>R    3?455551a=A1Q<??4    1Q<??32a=566662a=455551dy))))1e
++++1c?344441d566661d566661e 788884!!"WXXXX4""#XYYYY4  !:As SSS4!!">????4!!"Ycdnq!rrr4""#Zdeor"sss4A!!"OPPPPr,   c                     S[         l        [        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      S:X  d   e[        SS	S5      S:X  d   e[        S
SS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SSS5      R                  S5      (       d   e[        SS[        -
  S5      R                  S5      (       d   eg )Nr   r   r
   r   r   r   i}  r   r   ir   i#  r   r	   r   r   gg:(Zr   r   y(.?-@:4@)r   r   
gegenbauerr   r$   r9   r,   r*   test_gegenbauerr    s=   BFa!####a!$$$$a!!!!a1"""b#q!$$T****aq!$$R((((aq!$$R((((aq!$$R((((dD!$''(>????dAaC&))*XYYYYr,   c                     S[         l        [        SSS5      [        SS5      :X  d   e[        SSS5      R	                  S5      (       d   e[        SSSS	S
9R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        S[
        -   S[
        * 5      R	                  S5      (       d   e[        S[
        -   S[
        * S	S
9R	                  S5      (       d   e[        SSS	5      R	                  S5      (       d   e[        SSS	S	S
9R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        SSSS	S
9R	                  S5      (       d   e[        S	SS	5      R	                  S5      (       d   e[        S	S	S	5      R	                  S5      (       d   e[        S	SS	5      R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   e[        SSS5      R	                  S5      (       d   eg )Nr   r
   r   r   r   r   r   gLXz?r   typey        LXz?r   gLXzr   yI:r AEZ;Aytp@&xsog9B.y        9B.?iy        H6u@yjA?jAr   y}$!}f?}$!}f?yb`3?b`3gFo)r   r   legenpr  r   r$   r9   r,   r*   test_legenpr    s>   BF!Aa=HQqM)))"b#!!"89999"b#A&))*ABBBB"a  !89999!A#taR ##$RSSSS!A#taRa(++,Z[[[[!Aa=A!AaQ""1%%%%!Ac?45555!Acq!$$%;<<<<!Aa=D!!!!!Aa=K((((!Aa=A!C?NOOOO"T! PQQQQ"SMNNNN"S!!"9::::r,   c            	      F   S[         l        [        n [        U " SSS5      5      (       d   e[        U " SSS5      5      (       d   e[        U " SSSSS95      (       d   e[        U " SSSSS95      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSSSS	S
9R	                  S5      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSSSS9R	                  [
        5      (       d   eU " SSSSS	S
9R	                  S5      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSSS	S9R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSSSS9R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSSS	S9R	                  S5      (       d   eU " SSS5      R	                  S5      (       d   eU " SSS5      R	                  S 5      (       d   eU " SSSSS9R	                  S!5      (       d   eU " SSSSS9R	                  S"5      (       d   eU " SSSSS9R	                  S#5      (       d   eU " SSSSS9R	                  S$5      (       d   eU " SSSSS9R	                  S!5      (       d   eU " SSSSS9R	                  S%5      (       d   eU " SSSSS9R	                  S#5      (       d   eU " SSSSS9R	                  S$5      (       d   eU " S&S'SSS9R	                  S(5      (       d   eU " S&S'SSS9R	                  S)5      (       d   eU " S*SS5      R	                  S+5      (       d   eU " S*SS5      R	                  S,5      (       d   eU " S*SS5      R	                  S-5      (       d   eU " S*SS5      R	                  S.5      (       d   eU " S*SS5      R	                  S/5      (       d   eU " S*SSSS9R	                  S05      (       d   eU " S*SSSS9R	                  S15      (       d   eU " S*SSSS9R	                  S25      (       d   eU " S*SSSS9R	                  S35      (       d   eU " S*SSSS9R	                  S45      (       d   eg )5Nr   r   r
   r   r   r  r   r   r   )r  r   r   g
Zy
Z@
Zr   y3A-DT!?r   gzr   r   gz?y3A?-DT!g3Ayz-DT!y       -DT!yz?-DT!g3A?y5Oϋ?!3|g{~
6yWFEi l@gaUO}2?gaUO}2yWFE?i ly       WfѷgWfѷg&D\4(y       &D\4(gWfѷ@r   r   yuFhZ?ǒsICy:QN?}U@x$?r@   y        <@gJj?gfFU?g 6Կy<P0(?y        P0(?y 6ԿJjyfFU?fFUyJj? 6?gP0(ӿ)r   r   legenqrx   r   r$   )fs    r*   test_legenqr"    sc   BFA1Qq???1Qr1Qqa!!!!1Qrq!""""Qq?b!!!!R!C(++A....S1! 67777Qq?a    R!C(++A....S1! <====Qq;>>IJJJJQq;>>12222QqC ##A&&&&Qq:==/0000Qq:==GHHHHQq1  !89999Qq1  !PQQQQQq?56666Qq! NOOOOQq! 67777Qq;>>HIIIIQq;>>12222Qq8;;r???Qq:==01111Qq:==GHHHHQq;>>IJJJJQq;>>01111QqC ##A&&&&Qq:==01111Qq:==GHHHHQq! 78888Qq! 67777Qq! 67777Qq! 78888Qq1  !89999Qq1  !67777Qq1  !78888Qq1  !89999T41%(()]^^^^T4A&))*\]]]]T!D>34444T!D>23333T!A;>>/0000T!C=34444T!C=KLLLLT!Da ##$;<<<<T!Da ##$STTTTT!A1  !OPPPPT!CQ""#QRRRRT!CQ""#:;;;;r,   c                     S[         l        [        SS5      S:X  d   e[        SS5      S:X  d   e[        SS5      S:X  d   e[        SS5      S:X  d   e[        [        [        5      [        :X  d   eS[        S[	        S5      5      -  R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S	5      (       d   e[        S[        5      R                  S
5      (       d   e[        S5      [        SS5      :X  d   e[        SS5      R                  S5      (       d   eg )Nr   r   r   r   r
   gDSYC?g=O?r   gN_?rn   r	   r   yk7WO?>I?)r   r   agmr$   rr   r   r9   r,   r*   test_agmr%  K  s   BFq8q==q8q==q8q==q8q==q8q==c!DGn  !56666q8;;,----q8;;,----q8;;ABBBBq6S1Xr!9<<?@@@@r,   c                     S[         l        [        SS5      R                  S[	        S5      -  5      (       d   e[        SSS5      R                  SS[	        S5      -  -
  5      (       d   e[        SSS5      R                  S	[	        S5      -  S
[	        S5      -  -   5      (       d   e[        SS5      R                  S5      (       d   e[        SSS
5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS[
        -   S[
        -
  5      R                  S5      (       d   e[        SS[
        -
  5      R                  S5      (       d   e[        SS
SS5      R                  S5      (       d   e[        SS[        5      R                  [        S5      5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SSS5      [        :X  d   e[        SSS 9R                  S!5      (       d   e[        SSS5      S:X  d   e[        SS[
        -   S[
        -
  5      R                  S"5      (       d   e[        S#S5      R                  S$5      (       d   e[        S%S%5      R                  S&5      (       d   e[        S'S%5      R                  S(5      (       d   e[        SS%5      R                  S)5      (       d   e[        S*S%5      R                  S+5      (       d   e[        [        SSSS,95      (       d   e[        S%SSS,9[        :X  d   e[        SSSS,9S:X  d   e[        SSSS,9S:X  d   e[        SS-SS,9S:X  d   e[        SS.SS,9S:X  d   e[        SS/SS,9S:X  d   e[        S%SSS,9S:X  d   e[        S%S.SS,9S:X  d   e[        S%S/SS,9S:X  d   e[        S%SSS,9S:X  d   e[        S%S0SS,9S:X  d   e[        S%S1SS,9S:X  d   e[        S%S2SS,9S:X  d   e[        SSSS,9R                  [	        S5      5      (       d   e[        SS.SS,9R                  [	        S05      5      (       d   e[        SS/SS,9R                  [	        S15      5      (       d   e[        SS2SS,9R                  [	        S35      5      (       d   e[        S4S5      R                  S5SS6[        -  S79(       d   e[        S4SSS,9S:X  d   e[        S4S25      R                  S8SS6[        -  S79(       d   e[        S4S2SS,9S:X  d   e[        S-S9SS,9R                  S:5      (       d   e[        S;S;SS,9R                  S<5      (       d   e[        SS
S5      [        SSS
5      * :X  d   e[        S
SS5      R                  S=5      (       d   e[        S
SSSS,9R                  S>5      (       d   e[        SSS5      R                  S?5      (       d   e[        SSSSS,9S:X  d   e[        S%SS5      R                  S@5      (       d   e[        S%SSSS,9S:X  d   e[        SSS5      R                  S?5      (       d   e[        SSSSS,9S:X  d   e[        SSASB5      R                  SCSS6[        -  S79(       d   e[        SASS5      R                  SD5      (       d   e[        SSE5      S:X  d   e[        SSF5      S:X  d   e[        SS%5      S:X  d   e[        SSG5      S:X  d   e[        SHS%5      S:X  d   eg )INr   r
   r   rR   r   r   r   r   r   r   r	   r@   r   y!?03Dg66?r   yr?̿yt2?c:?Tg\$?r   g     b  z6.9825435345798951153e-627i   z4.6885137549474089431e-788r   g     4y
 I?Byg     iy
 I?licp)bgdT:?y       Ƿҿr   g8,6V@r   yC\W-DT!	@r   yN(T?-DT!yGfs-8R?r   y}?fs-8R)regularizedr   i  l       73Me'r   l    73Me'r   rm   z1.3669297209397347754e-301037r[   r   z>-1.322575609404222361e-698979 - 4.9274570591854533273e-698978jy      @      @y]y7޵?WHy             @@yK!:#H? \h?gٕK&?g|"?g]5[?g +?r   i.  z1.1359381951461801687e-4327z8.1244514125995785934e4765y            y            ?r   r   )
r   r   gammaincr   rc   r$   r#   rq   rx   r   r9   r,   r*   test_gammaincr,  Y  su   BFAa=Ac"gI&&&&Aa?a#b'	k****Aa?bRj3r723333D!!"OPPPPAa?56666Aa=34444Aac!A#!!"PQQQQAac?LMMMMAa$""#9::::C#!!%*----F3""#?@@@@F3""#?@@@@D% ##$QRRRRD&!$$%TUUUUAa?c!!!A?34444Aa?aAac!A#!!":;;;;D45555Br?MNNNNBr?LMMMMBr?MNNNNBr?NOOOO!QD12222Bt,333Aqd+q000Aqd+q000At.!333At.!333Av40A555Bt,111B$/1444BD1Q666B-222B40A555BT2a777B$/1444Aqd+..s2w7777At.11#e*====Av4033CLAAAAAt.11#e*====HQ""#BAWXY\W\"]]]HQ40A555HT"%%&fpq{|  ~A  |A%  B  B  BHTd3q888D$D1445effffE5d3667ghhhhAa?x!A....Aq! 56666Aq!.112HIIIIAq! 78888Aq!.!333B1  !89999B1$/1444Aq! 78888Aq!.!333Aue$''(EqZ[\_Z_'```E1a ##$@AAAAAe!!!Ae!!!Ab>QAe!!!D!!!r,   c                  Z   S[         l        [        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S	S5      R                  S
5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S	S5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  SS	S[        -  S9(       d   e[        SS5      R                  SS	S[        -  S9(       d   e[        SS5      R                  SS	S[        -  S9(       d   e[        S	S5      R                  SS	S[        -  S9(       d   e[        SS5      R                  S S	S[        -  S9(       d   e[        SS5      R                  S!S	S[        -  S9(       d   e[        SS5      R                  S"S	S[        -  S9(       d   e[        SS#5      R                  S$5      (       d   e[        SS#5      R                  S%5      (       d   e[        SS#5      R                  S&5      (       d   e[        S	S#5      R                  S'5      (       d   e[        SS#5      n U R                  S(5      (       d   eU R
                  R                  S)5      (       d   e[        SS#5      n U R                  S*5      (       d   eU R
                  R                  S+5      (       d   e[        SS#5      n U R                  S,5      (       d   eU R
                  R                  S-5      (       d   e[        SS.5      R                  S/S	S[        -  S9(       d   e[        SS.5      R                  S/S	S[        -  S9(       d   e[        SS.5      R                  S/S	S[        -  S9(       d   e[        S	S.5      R                  S/S	S[        -  S9(       d   e[        SS.5      R                  S/S	S[        -  S9(       d   e[        SS.5      R                  S/S	S[        -  S9(       d   e[        SS.5      R                  S/S	S[        -  S9(       d   e[        SS05      R                  S15      (       d   e[        SS05      R                  S15      (       d   e[        SS05      R                  S15      (       d   e[        S	S05      R                  S15      (       d   e[        SS05      n U R                  S15      (       d   eU R
                  R                  S)5      (       d   e[        SS05      n U R
                  R                  S25      (       d   eU R                  S15      (       d   e[        SS05      n U R
                  R                  S35      (       d   eU R                  S15      (       d   e[        SS5      R                  S45      (       d   e[        SS5      R                  S55      (       d   e[        SS5      R                  S65      (       d   e[        S	S5      R                  S5      (       d   e[        SS5      R                  S75      (       d   e[        SS5      R                  S85      (       d   e[        SS5      R                  S95      (       d   e[        SS5      R                  S:5      (       d   e[        SS5      R                  S;5      (       d   e[        SS5      R                  S<5      (       d   e[        S	S5      R                  S5      (       d   e[        SS5      R                  S=5      (       d   e[        SS5      R                  S>5      (       d   e[        SS5      R                  S?5      (       d   e[        SS5      R                  S@S	S[        -  S9(       d   e[        SS5      R                  SAS	S[        -  S9(       d   e[        SS5      R                  SBS	S[        -  S9(       d   e[        S	S5      R                  S S	S[        -  S9(       d   e[        SS5      R                  SCS	S[        -  S9(       d   e[        SS5      R                  SDS	S[        -  S9(       d   e[        SS5      R                  SES	S[        -  S9(       d   e[        SS#5      n U R                  SF5      (       d   eU R
                  R                  SG5      (       d   e[        SS#5      n U R                  SH5      (       d   eU R
                  R                  SI5      (       d   e[        SS#5      n U R                  SJ5      (       d   eU R
                  R                  SK5      (       d   e[        S	S#5      n U R                  S(5      (       d   eU R
                  R                  S)5      (       d   e[        SS#5      n U R                  SL5      (       d   eU R
                  S	:X  d   e[        SS#5      n U R                  SM5      (       d   eU R
                  S	:X  d   e[        SS#5      n U R                  SN5      (       d   eU R
                  S	:X  d   e[        SS.5      R                  SOS	S[        -  S9(       d   e[        SS.5      R                  SPS	S[        -  S9(       d   e[        SS.5      R                  SQS	S[        -  S9(       d   e[        S	S.5      R                  S/S	S[        -  S9(       d   e[        SS.5      R                  SRS	S[        -  S9(       d   e[        SS.5      R                  SSS	S[        -  S9(       d   e[        SS.5      R                  STS	S[        -  S9(       d   e[        SS05      n U R                  SU5      (       d   eU R
                  R                  SG5      (       d   e[        SS05      n U R                  SV5      (       d   eU R
                  R                  SI5      (       d   e[        SS05      n U R                  SW5      (       d   eU R
                  R                  SK5      (       d   e[        S	S05      n U R                  S15      (       d   eU R
                  R                  S)5      (       d   e[        SS05      R                  SX5      (       d   e[        SS05      R                  SY5      (       d   e[        SS05      R                  SZ5      (       d   eg )[Nr   r	   r   gb?r   gkӦ?r   gzCⷆ?r   g_mv?r   g/ɫ|?r
   gslR
w?r   gAt?r   g_gʩPfgLX!tghĊJQ"yʹ+-DT!	y[!z?/u%y.%2l>3i^  gԇqir[   r   g+{gգ; jg{/1XgK];@}Fg.H4go:ɴ`#igptOgc_g8>VpgYògoZg-DT!	gTk gԚ:.gF@g_wf4}l     =RM!	 z/2.1592908471792544286e-152003068666138139677919l  =RM!	 z0-3.7805306852415755699e+152003068666138139677871ggתECgE{D?g>EӦu:?g:([?gf?g d?g?yVR!i?fs-8R?y+B\*-DT!yTj@-DT!	@gk9!ǎ@@gƇxTg~8n@g9blBg1*jg/nQgJ` g_A g?Ho!ga]gfs-8R?g&\Ig-DT!g`VAGp^g-DT!	@gj<~_g/p8gK`z/5.0362468738874738859e-152003068666138139677990z/1.7626864058606158601e-152003068666138139677966z/6.1694024205121555102e-152003068666138139677943z,7.5575179651273905e-152003068666138139677896z.2.645131287794586675e-152003068666138139677872z/9.2579595072810533625e-152003068666138139677849z/8.8175642804468234866e+152003068666138139677800z0-3.0861474981563882203e+152003068666138139677824z/1.0801516243547358771e+152003068666138139677848z/1.3231857398345514495e+152003068666138139677895z0-4.6311500894209300731e+152003068666138139677918z/1.6209025312973255256e+152003068666138139677942)r   r   r   r   r   rw   r+  )r   s    r*   test_gammainc_expint_nr.    s2    BF"S>45555"S>45555"S>45555!C=45555!C=45555!C=45555!C=45555"T?45555"T?45555"T?45555!D>34444!D>LMMMM!D>KLLLL!D>LMMMM"S>7AcERRR"S>7AcERRR"S>7AcERRR!C=61S5QQQ!C=61S5QQQ!C=61S5QQQ!C=61S5QQQ"T?9::::"T?9::::"T?9::::!D>89999qA44+,,,,6699+,,,,qA44+,,,,6699+,,,,qA44+,,,,6699+,,,,"-.112cmnxyz}x}1~~~"-.112cmnxyz}x}1~~~"-.112cmnxyz}x}1~~~!,-001blmwxy|w|0}}}!,-001blmwxy|w|0}}}!,-001blmwxy|w|0}}}!,-001blmwxy|w|0}}}"./223effff"./223effff"./223effff!-.112deeeeq*+A44BCCCC6699+,,,,q*+A6699/000044BCCCCq*+A6699/000044BCCCCBs89999Bs89999Bs78888Ac?67777Ac?45555Ac?45555Ac?45555Bt PQQQQBt PQQQQBt NOOOOAdNOOOOAd45555Ad56666Ad45555Bs91aPSeTTTBs8!QsUSSSBs8!QsUSSSAc?8!QsUSSSAc?8!QsUSSSAc?7AcERRRAc?8!QsUSSSDA44*++++6699+,,,,DA44+,,,,6699+,,,,DA44*++++6699*++++4A44+,,,,6699+,,,,4A44*++++66Q;;4A44+,,,,66Q;;4A44*++++66Q;;B/0334eopz{|z3  A  A  AB/0334eopz{|z3  A  A  AB/0334eopz{|z3  A  A  AA./223dnoyz{~y~2A./223aklvwx{v{2|||A./223cmnxyz}x}2~~~A./223dnoyz{~y~2-.A44ABBBB6699+,,,,-.A44BCCCC6699+,,,,-.A44ABBBB6699*++++,-A44BCCCC6699+,,,,A/0334effffA/0334fggggA/0334effffr,   c                      S[         l        [        SSSS5      R                  S5      (       d   e[        SSS	S
5      R                  S5      (       d   e[        SSSS
5      R                  S5      (       d   eg )Nr   r   r	   r   r   gO@r  y      ?       @r   rR   y	?f,?r   r   r   gX|W'@)r   r   betaincr   r9   r,   r*   test_incomplete_betar1  $  sr    BF2bT"%%&?@@@@3vc!$''(bcccc1Qq9::::r,   c                  ~   S[         l        [        S5      S:X  d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        [        5      R                  S	5      (       d   e[        S
5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        [        S5      [        5      (       d   e[        [        S5      [        5      (       d   e[        [        S5      [        5      (       d   e[        [        S5      [        5      (       d   e[        [        5      S:X  d   e[        [        * 5      S:X  d   e[        S5      S:X  d   e[        S[        -  5      R                  S5      (       d   e[        [        5      [        :X  d   e[        [        * 5      [        * :X  d   e[        S5      [        S5      :X  d   e[        S5      [        S5      :X  d   e[        S5      R                  S[        S5      -
  5      (       d   e[        S5      S:X  d   e[        S5      R                  S[        S5      -
  5      (       d   e[        S5      R                  S[        S5      -
  5      (       d   e[        S[        -  5      R                  S[        S[        -  5      -
  5      (       d   e[        S5      S:X  d   e[        S5      S:X  d   e[        [        * 5      S:X  d   e[        [        5      S:X  d   e[        [        [        5      5      (       d   e[        S5      [        S5      S-  -  R                  S5      (       d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        S5      R                  S5      (       d   eS[         l        [        S5      SS -  -  R                  S!5      (       d   e[        S5      SS"-  -  R                  S#5      (       d   eS[         l        [        [        SS-  5      5      S$:X  d   e[        S5      S:X  d   e[        S%5      R                  S&5      (       d   e[        S'5      R                  S(5      (       d   e[        S5      [        :X  d   e[        S5      [        * :X  d   e[        [        S)5      5      R                  S)5      (       d   e[        [        S*5      5      R                  S*5      (       d   e[        [        S+5      5      R                  S+5      (       d   eS[         l        [        [        S,5      5      R                  S,5      (       d   e[        [        S-5      5      R                  S-5      (       d   e[        [        S.5      5      R                  S.5      (       d   eS[         l        [        S/5      n U R                  S:X  d   eU R                   R                  S05      (       d   e[        S15      R                  S5      (       d   e[        S25      SS3-  -  R                  S45      (       d   e[        S55      R                  S65      (       d   eg )7Nr   r   r   gAg?r   y^u;y            yxGDY$W
?g|b?r   y        .($h?             y       .($hr                   gL:?ri   y?      ?ro   r
   r*  r   r   iMz3.63998738656420y       @      "@y%?@[09Ay%?@[0A9y             "y%?@[09Ar0   -   z32.0884875837625447570007862949577886115608181193212i@  z32.0709207788416560484484478751657887929322509209954zv3.66744826532555e-4342944819032518276511289189166050822943970058036665661144537831658646492088707747292249493384317534r   g
$?r   g
$޿r   gP?gPz"0.99999999999999999999999999999995z#0.999999999999999999999999999999995z$-0.999999999999999999999999999999995r   z-6.1481820666053078736e+1083y      Y      @y      Y@      @i  y?}d-@OB+xr   yWMYA`E?m<p)r   r   erfr   r   rs   r&   rd   r#   erfierfcrx   ry   r   erfinvrv   rw   re   s    r*   test_erfr:  *  sv   BFq6Q;;q699+,,,,t9<<HIIIIu:==JKKKKr7::,----r7::,----s8;;.////c!fc""""c"gs####c!fc""""c"gs####s8q==t9??7a<<":==-....9:#t9A:a   x=AX.////7a<<7::aAh8;;qRy!!!!":==3qt9%%%%9>>>Q:??9>>cKB))--.@AAAAt9<<GHHHH:==GHHHH;>>IJJJJBFHRVO UVVVVHRX!!"WXXXXBFtBF|  !Y  Y  Y  Y!9>>#;>>01111$<??23333!9":#vd|%%%%vn%&)).9999vo&'**?;;;;BFv:;<??@deeeev;<=@@Afggggv<=>AABhiiiiBFS	A66Q;;669934444=ALT!%%&TUUUU>RSSSSr,   c                     S[         l        [        [        * 5      S:X  d   e[        [        5      S:X  d   e[        SSS5      R	                  [        SSS5      5      (       d   e[        S [        * [        /5      S:X  d   e[        S5      S	:X  d   e[        S
S
5      S	:X  d   e[        [        * 5      S:X  d   e[        [        5      S:X  d   e[        S5      S:X  d   e[        S5      S-  R	                  S5      (       d   eg )Nr   r   r   r
   r   r   c                     [        U SS5      $ )Nr   g?)npdfr   s    r*   <lambda>test_pdf.<locals>.<lambda>n  s    D4,r,   r   r   r   r   ro         B3v^!< gwbLz@)r   r   r=  r#   r   quadtsncdfr9   r,   r*   test_pdfrD  i  s    BF:??9>>!A;>>$s1Q-((((,tSk:a???7c>>!9:??9>>8q==If  !23333r,   c                     S[         l        [        S5      S:X  d   e[        S5      S:X  d   e[        [        5      [        :X  d   e[	        [        [
        5      5      (       d   e[        [        S5      R                  [        :X  d   e[        [        S5      R                  R                  S[        -  5      (       d   e[        [        * S5      R                  [        :X  d   e[        [        * S5      R                  R                  S[        -  5      (       d   e[        SS5      [        * :X  d   e[        SS5      [        * :X  d   e[        SS5      [        * :X  d   e[        [        5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        [        * S-  5      R                  [        [        -  S-  5      (       d   e[        [        S5      * S-  5      R                  [        S5      * 5      (       d   e[        S	5      R                  S
5      (       d   e[        S5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S	S5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S	S5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        SS5      R                  S5      (       d   e[        S5      R                  S5      (       d   e[        S5      R                  S 5      (       d   e[        SS5      R                  S!5      (       d   e[        SS5      R                  S"5      (       d   e[        S#S5      R                  S$5      (       d   e[        SS5      R                  S%5      (       d   e[        SS5      R                  S&5      (       d   e[        SS'5      R                  S(5      (       d   e[        S)S*5      R                  S+5      (       d   e[        S)S5      R                  S,5      (       d   e[        S[        -   S--  5      R                  S.5      (       d   e[        S[        -   S--  S5      R                  S/5      (       d   e[        S[        -   S--  S5      R                  S05      (       d   e[        S[        -   S--  S*5      R                  S15      (       d   e[        S[        -   * S--  5      R                  S25      (       d   e[        S[        -   * S--  S5      R                  S35      (       d   e[        S[        -   * S--  S5      R                  S45      (       d   e[        S[        -   * S--  S*5      R                  S55      (       d   eS6[         l        [        [        5      R                  S75      (       d   eS[         l        [        S85      R                  S95      (       d   e[        S:5      R                  S;5      (       d   e[        S<5      R                  S=5      (       d   e[        S>5      R                  S?5      (       d   e[        S@5      R                  SA5      (       d   e[        SSB5      n U R                  R                  SC5      (       d   eU R                  R                  SD5      (       d   eg )ENr   r   r4  r   r
   r   r   gW	&?r   g{?g      пgֿg-C6g"{,7gѤX9yHgtm3]NyHgtm3]N@y}&@r   yӸ?~dY?yg[忼@yӸ?~dYr   gr6@yAj@T'>@yAj@T'>r   y(o-@n!=@r   yAF?Z|?yٿ?y)u%+?y(tmȻy@yO^?"r   y~}?hey:㢥'%K8@g8	U'r   y:㢥'%K8gh㈵r   yk)j^-xe/:@yb/.>ꮺF@@r   y0j;?"B`?ym.[	<?@ysqM1mPyE&\57@y#u*Ϳ-pFſy>M|Wn2?yǁc'FyEyfI3I5fԪ4@r0   z81.073658194796149172092178407024821347547745350410314531y      Mb`?y7W@;ūԎ?y      Mb`y7W@;ūԎyy&1ܿ?y)!faYNJuM?yy&1ܿٿy)!faYNJuMyʡE-C6?yQW
㿘"1k?r   gQGg[[AD)r   r   lambertwr#   rx   ry   rv   rw   r   r   r   r$   log)r   s    r*   test_lambertwrH  w  s   BFA;!D>QC=C#C?3&&&C?""1R4((((SD  C'''SD  ##AbD))))Ab>cT!!!Aa=SD   Aa=SD   A;>>!A;>>.////RCE?ad1f%%%%SVGAI!!3q6'****D>12222E?34444Ia ##$<====E"  !56666D IJJJJE"  !56666DHIIIIE! IJJJJB<??CDDDDBq>FGGGGBr?FGGGGD>01111DGHHHHD HIIIIDFGGGGD>GHHHHI!!"KLLLLDHIIIID HIIIID KLLLLIa ##$NOOOOIb!$$%9::::Ib!$$%OPPPPJq!$$%NOOOOJq!$$%TUUUUQqS"H  !KLLLLQqS"HQ""#LMMMMQqS"HR ##$MNNNNQqS"HQ""#KLLLLacF2I!!"MNNNNacF2Ia ##$MNNNNacF2Ib!$$%NOOOOacF2Ia ##$LMMMMBFB<??UVVVVBFK ##$UVVVVK ##$UVVVVK ##$UVVVVK ##$UVVVV$%(()Z[[[[6A6699+,,,,6699.////r,   c                  X   S n S[         l        U " [        S5      S5      (       d   eU " [        S5      S5      (       d   eU " [        S5      S5      (       d   eU " [        S	5      S
5      (       d   eU " [        SS5      S5      (       d   eU " [        SS5      S5      (       d   eU " [        SS5      S5      (       d   eU " [        S	S5      S5      (       d   eU " [        SS5      S5      (       d   eU " [        SS5      S5      (       d   eU " [        SS5      S5      (       d   eU " [        S	S5      S5      (       d   eS nS nS nS nS[         l        S[        -  S[        -  -   n[        S5      n[        S5      n[        S5      n[        S5      n	[        S5      n
[        S 5      n[        S!5      nS[         l        U " [        U" XV5      5      S"5      (       d   eU " [        U" XW5      5      S#5      (       d   eU " [        U" XX5      5      S$5      (       d   e[        U" XY5      5      S:X  d   e[        U" XZ5      5      S:X  d   e[        U" X[5      5      S:X  d   e[        U" X\5      5      S:X  d   eU " [        U" XV5      5      S%5      (       d   eU " [        U" XW5      5      S&5      (       d   eU " [        U" XX5      5      S'5      (       d   eU " [        U" XY5      5      S(5      (       d   eU " [        U" XZ5      5      S)5      (       d   eU " [        U" X[5      5      S*5      (       d   eU " [        U" X\5      5      [        SS+5      5      (       d   eU " [        U" XV5      5      S,5      (       d   eU " [        U" XW5      5      S-5      (       d   eU " [        U" XX5      5      S.5      (       d   eU " [        U" XY5      5      S/5      (       d   eU " [        U" XZ5      5      S05      (       d   eU " [        U" X[5      5      S15      (       d   eU " [        U" X\5      5      [        S2S35      5      (       d   eU " [        U" XV5      5      S45      (       d   eU " [        U" XW5      5      S55      (       d   eU " [        U" XX5      5      S65      (       d   eU " [        U" XY5      5      S75      (       d   eU " [        U" XZ5      5      S85      (       d   eU " [        U" X[5      5      S95      (       d   eU " [        U" X\5      5      [        S2S:5      5      (       d   eU " [        U" XV5      S5      S;5      (       d   eU " [        U" XZ5      S5      S<5      (       d   eU " [        U" X[5      S5      S<5      (       d   eU " [        U" X\5      S5      S<5      (       d   eU " [        U" XV5      S5      S=5      (       d   eU " [        U" XW5      S5      S>5      (       d   eU " [        U" XX5      S5      S?5      (       d   eU " [        U" XY5      S5      S/5      (       d   eU " [        U" XZ5      S5      S05      (       d   eU " [        U" X[5      S5      S15      (       d   eU " [        U" X\5      S5      [        S2S35      5      (       d   eU " [        U" XV5      S5      S@5      (       d   eU " [        U" XW5      S5      SA5      (       d   eU " [        U" XX5      S5      SB5      (       d   e[        U" XY5      S5      S:X  d   e[        U" XZ5      S5      S:X  d   e[        U" X[5      S5      S:X  d   e[        U" X\5      S5      S:X  d   eU " [        U" XV5      S5      SC5      (       d   eU " [        U" XW5      S5      SD5      (       d   eU " [        U" XX5      S5      SE5      (       d   eU " [        U" XY5      S5      SF5      (       d   eU " [        U" XZ5      S5      SG5      (       d   eU " [        U" X[5      S5      SH5      (       d   eU " [        U" X\5      S5      [        SSI5      5      (       d   eU " [        U" XV5      S5      SJ5      (       d   eU " [        U" XW5      S5      SK5      (       d   eU " [        U" XX5      S5      SL5      (       d   eU " [        U" XY5      S5      S75      (       d   eU " [        U" XZ5      S5      S85      (       d   eU " [        U" X[5      S5      S95      (       d   eU " [        U" X\5      S5      [        S2S:5      5      (       d   eU " [        U" XV5      S5      SM5      (       d   eU " [        U" XW5      S5      SN5      (       d   eU " [        U" XX5      S5      SO5      (       d   eU " [        U" XY5      S5      SO5      (       d   eU " [        U" XZ5      S5      SO5      (       d   eU " [        U" X[5      S5      SO5      (       d   eU " [        U" X\5      S5      SO5      (       d   eSP[         l        S[        -  [        SQ5      -   nSRnS[         l        [        U5      R                  U5      (       d   eSS[         l        [        U5      R                  U5      (       d   eST[         l        [        U5      R                  U5      (       d   eg )UNc                    [        U5      nSn[        U[        5      (       a  [        U [        5      n[        U R                  UR                  -
  5      [        UR                  5      S-  [
        -  :*  n[        U R                  UR                  -
  5      [        UR                  5      S-  [
        -  :*  nU=(       a    U$ )NTr[   )convertrs   r&   r   rv   r   rw   )r   r   type_okreal_okimag_oks        r*   check!test_lambertw_hard.<locals>.check  s    AJa C(GaffQVVm$AFFAc(99affQVVm$AFFAc(99"7"r,   r   绽|=gj|=g|۽g|۽y        |=y#B;|=y       |۽y#B;|۽r   yM:
@y6S:8@y",KP:(*3@y.5L:(vf?r   yM:
g,qŔK:y.5L:(vfy",KP:(*3c                     [        XSS9$ NTr   )faddr   r   s     r*   r?  $test_lambertw_hard.<locals>.<lambda>      tAd+r,   c                     [        XSS9$ rS  )fsubrU  s     r*   r?  rV    rW  r,   c           	      *    [        U [        USSS9SS9$ )Nr   Tr   rT  r   rU  s     r*   r?  rV    s    QtAbt44@r,   c           	      *    [        U [        USSS9SS9$ )Nr3  Tr   r[  rU  s     r*   r?  rV    s    QtAc5DAr,     r   z1e-3z1e-10z1e-20z1e-40z1e-80z1e-300r   gmPPWg-gByejZ~,F2)ܲ?yr>y      a>=y      &;y      _}eO7y       z2.33164398159712420336e-500yʁ:UY 8ɩ?yu~l|H-I>yWѨ=y      {Kv;y      {S犹7y      ^{=o r   z1.64872127070012814684865e-500yʁ:UY 8ɩyu~l|H-IyWѨy      {Kvӻy      {S犹y      ^{=oՠz-1.64872127070012814684865e-500y,+@/c@yIS[@yQ}]t餫?yEI <ZI>yvT   =gj蚸5g4s g   yejZ~,F2)ܲyry      a>y      &ۻy      _}eOy      ޠz-2.33164398159712420336e-500yQ}]t餫yEI <ZIyvT   y,+@/cy SwyIS[r'  z1e-13z-0.99999926266961377166355784455394913638782494543377383744978844374498153493943725364881490261187530235150668593869563168276697689459394902153960200361935311512317183678882r0      )r   r   rF  r   r   r&   rd   r   )rO  addsubaddjsubjad3d10d20d40d80d300d1000r   anss                  r*   test_lambertw_hardrl    s$
   # BF%":;;;;&!#<====&!#\]]]]'"$]^^^^%"$RSSSS&#%STTTT&#%STTTT'!$&TUUUU%#%STTTT&$&<====&$&UVVVV'"%'UVVVV ,C
+C@DADBF
1r#vA	VB
g,C
g,C
g,C
g,Cx=D	NEBF #a)$&=>>>>#a*%'>????#a*%'>????CJ2%%%CJ2%%%CK B&&&CL!R'''#a)$&UVVVV#a*%'`aaaa#a*%'^____#a*%'GHHHH#a*%'GHHHH#a+&(IJJJJ#a,'R0M)NOOOO$q*%'VWWWW$q+&(abbbb$q+&(_````$q+&(_````$q+&(MNNNN$q,')OPPPP$q-(#d3S*TUUUU$q*%'VWWWW$q+&(abbbb$q+&(_````$q+&(_````$q+&(MNNNN$q,')OPPPP$q-(#d3T*UVVVV$q*Q')bcccc$q+a(*cdddd$q,q)+deeee$q-*,effff$q*Q')deeee$q+a(*jkkkk$q+a(*ghhhh$q+a(*fgggg$q+a(*OPPPP$q,q)+QRRRR$q-*C6V,WXXXX #a)B')DEEEE#a*R(*EFFFF#a*R(*EFFFFCJr"b(((CJr"b(((CK#r)))CL$***#a)B')XYYYY#a*R(*cdddd#a*R(*abbbb#a*R(*JKKKK#a*R(*JKKKK#a+b)+LMMMM#a,r*C3Q,RSSSS$q*R(*effff$q+b)+fgggg$q+b)+effff$q+b)+hiiii$q+b)+PQQQQ$q,r*,RSSSS$q-+S6W-XYYYY$q*R(*abbbb$q+b)+bcccc$q+b)+bcccc$q+b)+bcccc$q+b)+deeee$q,r*,effff$q-+-fggggBF
1s7|A=C BFA;>>#BFA;>>#BFA;>>#r,   c                     S[         l        [        SS/S//SS/SS//S5      R                  S5      (       d   e[        / S[        -   //S/S//S	5      R                  S
5      (       d   e[        S/S//S/S//S5      S:X  d   e[        S// // SQ/ /S5      R                  S5      (       d   e[        S/S//S/S//S5      R                  S5      (       d   e[        S/S//S/S//S5      R                  S5      (       d   e[        S/S//S/S//S5      R                  [
        S-   * S[
        -  -  5      (       d   eSn Sn[        S5      [        S5      4 H  n[        XU5      n[        U5      [        U 5      -  [        SU -
  // /S/SU-
  //U* 5      -  n[        U5      [        U 5      -  [        S/SSU-
  -
  //SSU -
  -
  // /SU-  5      -  nUR                  U5      (       d   eUR                  U5      (       a  M   e   g )Nr   r
   r   r   r   r   r   g%WV@r   yc2hp@'4Dr   r   )r   r   r   z2/3z2/27gmD@r	   r   r   r@   gyhr   r   g       r   )	r   r   meijergr   r$   r   r&   r]   rq   )rc  r(  r   x1x2x3s         r*   test_meijergrr  :  s4   BFQqE1#;Q14778MNNNNB!u:sA3i.112`aaaaTFA3<#sA.!333QC8.3V<??@UVVVVRD$=B4-699:UVVVVVHhZ(F8XJ*?FIIJeffffRD$=B4-477"Q$2GGGGAA$iQ A]1XeAhw1bzA3!u+qbAA1XeAhwq!A#wi'81ac7)B1MMuuRyyyuuRyyy !r,   c                     S[         l        [        SSSSSS5      R                  S5      (       d   e[        SSSSSS5      R                  S5      (       d   e[        SSSSSS	5      R                  S
5      (       d   e[        SSSSSS5      R                  S5      (       d   e[        SSSSSS5      R                  S5      (       d   eg )Nr   r
   r   r   r   g      ir   r   r      r   g      ?gk?)r   r   appellf1r   r9   r,   r*   test_appellf1rv  M  s    BFAb1Qq!$$U++++Aa1Qq!$$R((((Aa1S&))#....Bq1Qq!$$R((((Aa!C&))+ABBBBr,   c                  t    S[         l        [        [        SS5      SS5      R	                  S5      (       d   eg )Nr   r   r   r
   r   gpu4@)r   r   coulombgrd   r   r9   r,   r*   test_coulombry  U  s2     BFC1Ia"%%&;<<<<r,   c                     S[         l        [        SS5       V s/ s H  o S-   PM	     nn [        SS5       V s/ s H  o S-   PM	     nn [        XS5      R	                  S5      (       d   e[        SS	S
5      R	                  S5      (       d   e[        SSS5      S-  R	                  S5      (       d   e[        SSSS5      S-  R	                  S5      (       d   e[        SSSS5      SS-  -  R	                  S5      (       d   e[        SSSSSS9S:X  d   e[        SSS	5      SS-  -  R	                  S 5      (       d   e[        SSSS!S"S#9SS$-  -  R	                  S%5      (       d   e[        S&SS
5      S:X  d   e[        R                  " [        S' 5        [        S( S/S)S*9[        :X  d   e[        / / // S+Q/ /S,5      R	                  S-5      (       d   e[        S.S.5      SS/-  -  R	                  S05      (       d   eS1[         l        [        S2S3S	5      SS4-  -  R	                  S55        [        S6S3S	5      SS4-  -  R	                  S75        S[         l        [        S2S3S	5      SS4-  -  R	                  S55        [        S6S3S	5      SS4-  -  R	                  S75        [        [!        S8S9S:S;9S
5      R	                  S<5      (       d   e[        S8SS	-  -  S-   SS	-  4S
5      R	                  S<5      (       d   eg s  sn f s  sn f )=Nr   r   r   rQ  ir   gũܘ8Vr   r   r   gN*r   r   r  rA  gP+(	@i|g      %@gGz?gS?r   r   r     g_?r   r'  r   r   ii  g{<      r   )maxterms   g~bf86r
   c                      [        S S/5      $ )Nc                     / / / / U /U * /S4/$ Nr   r9   rc  s    r*   r?  =test_hyper_param_accuracy.<locals>.<lambda>.<locals>.<lambda>h  s    Br"RaRDQT;U:Vr,   r   )	hypercombr9   r,   r*   r?  +test_hyper_param_accuracy.<locals>.<lambda>h  s    i0VYZX[&\r,   c                     / / / / U /U * /S4/$ r  r9   r  s    r*   r?  r  i  s    Br"aS1"c :;r,   r   )infprec)r   r   r   r   r   giաe?i  ^   gL?r   g    r]  r   g{	!@r   gL`L"@r   z1e-100Tr   g;.ɂQ)J)r   r   r(   rb   r   r  r]   r_   pytestraises
ValueErrorr  r#   rn  r'   r\   rT  )r)   AsBss      r*   test_hyper_param_accuracyr  [  s   BF B<	(<aE'<B	( R=	)=aE'=B	)r?56666#sD!$$%@AAAA4$&**+@AAAA2tT4(/334IJJJJ4D&r3w.223IJJJJ"b!S3/144464%b#g-112HIIII4D7C?CCDZ[[[[!Q"""
MM*\];aS#NRUUUUBr7Ib>#.112GHHHHCRV#''(=>>>>BFGT3C'++,ABE4b#g%))*?@BFGT3C'++,ABE4b#g%))*?@$s8$/699:QRRRR3r3w;q="c'*D1445LMMMM- 
)	)s
   K:K?c                      [        S S/5      S:X  d   e[        S// /S/S//S5      R                  S5      (       d   eg )Nc                     S/U // / / / S44$ )Nr   r9   r  s    r*   r?  )test_hypercomb_zero_pow.<locals>.<lambda>w  s    !aSBr"Q 79r,   r   r   r   r|  g2}$?)r  rn  r   r9   r,   r*   test_hypercomb_zero_powr  u  sI    9A3?1DDDTF2;UG}Q/223HIIIIr,   c                     S[         l        Sn Sn[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S	5      (       d   e[        SSX5      R                  S
5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      R                  S5      (       d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSX5      S:X  d   e[        SSSS5      R                  S5      (       d   e[        SS[        -
  S[        -   S 5      R                  S!5      (       d   e[        S"S#X5      R                  S$5      (       d   e[        S%SSS5      R                  S&5      (       d   e[        SSSS5      S:X  d   e[        S"SSS5      R                  S'5      (       d   e[        S"S(SS5      R                  S)5      (       d   e[        SSSS5      R                  S*5      (       d   e[        SSSS5      S:X  d   e[        SSSS5      R                  S+5      (       d   eg ),Nr   r   r   r   gmBP?r   r   yGL?bD:Ig9^Gq?yGLĿbD:Ir
   r   yi'K?vm)˥y4f'?=!gzߚs?y4f'Կ=!yi'K?vm)˥?r   r	   yf K9?hWyC(?6tMyHc?x+̣g'?yHcۿx+̣yC(?6tM?yf K9hWr   r   r  y6x0%@r   r   y@%DMjtr   r   y̝4?d[v/?r   yJ)?yE6鏿yo@-ſ?Tpkÿr   yN}}?z?gh?yەĿ  ֿ)r   r   	spherharmr   r$   )tr   s     r*   test_spherharmr  z  s   BFAQQq  !78888Qr!!!"RSSSSQq  !78888Qq  !RSSSSQr!!!"TUUUUQr!!!"RSSSSQq  !78888Qq  !RSSSSQq  !STTTTQr!!!"TUUUUQr!!!"RSSSSQr!!!"RSSSSQq  !78888Qq  !RSSSSQq  !QRRRRQq  !TUUUUQr!!###Qr!!###Qq"""Qq"""Qq"""Qq"""Qr!!###Qr!!###Qq"""Qq"""Qr!!###Qr!!###Qs3t$''(WXXXXT1Q3!T*--.]^^^^RA ##$TUUUUT1c4(++,^____RC&!+++RC&))*[\\\\Rc4(++,^____Qq1  !78888Qr!A!###Qr!A!!"STTTTr,   c                  `    S[         l        [        SSS5      R                  S5      (       d   eg )Nr   r
   r   r   z2.7291482267247332183e2391)r   r   qpr   r9   r,   r*   test_qfunctionsr    s'    BFa#;>>67777r,   c                      S[         l        [        SS5      n [        SSSSS5      R	                  S	5      (       d   eS
[         l        [        R                  " [        S 5        g )Nr^  l   L33F i   r{  r   g?r   z40.99999999999999999999996570910644857895771110649954r   c                      [        SSSS5      $ )Nr   r   r   )r_   r9   r,   r*   r?   test_issue_239.<locals>.<lambda>  s    fR#c&:r,   )	r   precldexpr0  r   r   r  r  r  r>  s    r*   test_issue_239r    sQ    BGs#A3Qa(++,bccccBF
MM*:;r,   r   )r.   gE.,[@glN!@gr D'@gq>-@g?12@gs-65@gV;Z8@g_T~;@gҾˑu>@goN@@gzcuB@g:)~zD@g]ƒE@g+G@)	ouU@Pr@)X$@*@6{x0@lA稝3@6@W9@q=@+knG@@|A@i#<C@bKsD@?k]1aF@gՊcG@)r/   g" @gd0v[='@g}-@g4	1@guԄ5@g&E8@gJk;@gb>@g[I@@gdrnB@g VD@gƗ_E@gMO$&G@gKd՘H@)g((I@gҤ#@g$c*@gT
590@goh3@g@-6@gmQڇ9@gZA<@gkM@@gvgA@g߬k/C@gc1D@gKw$UF@g"3G@gh{I@)g+lpvZ@g!!!&@gQj ,@g[w1@gV#4@gv8@gUsj2;@gv[^>@g۴@@guxYB@g?C@gC`(E@gCR9|G@g4|7H@gQa[<J@)g=!@gUф](@g7}f/@gy2@g76@gh*n9@gj<@gfϪ?@gb~A@gXvC@g?-ƩD@gO>F@gsiG@gѰz0QgI@gJtDJ@)gh_I#@gWp-+@gYdS 1@g~-=R4@gF+	7@gdz:@gv>@gOԝ@@g,6B@g6C@gWIcE@g|1[yF@gdюH@g`Z@%#J@gL'ReK@)gj8,&@gU}-@gjfLI2@gJC<5@goW8@g\0<@g+|=<l?@g@$QA@gX[B@gwodD@gMF@grtG@gFHI@g1rJ@gf S;sL@)gK?s(@g~	0@g{3@gu6@gMD:@gU)Z=@gDe@@giͺZGB@gƞC@gC:FP8E@gnF@g4iH@gv J@g
ҥK@gN-M@)gxGf*@g_u=1@g24@g};8@gsp;@g.2>@gLA@gJy6B@g]rtPD@giUXE@ge;G@gfI@gJ@gJgNOL@gNOM@)r1   g.yn2@gĜ;6@g$Yk9@g4&+<@gK@@gh\A@gqaC@g@N E@gK`8F@goWA<9H@g7j+I@gmK@g#!JM@g	 wN@)gó ./@g3@gǌYF7@g9bw:@g;->@g8_@@g%):wjB@gו9PD@gZ]s&E@gkJMG@gRH@gvJ@g&[0 L@gmM@gud[SO@)gO0@gwpM74@gFɰ~8@gŜv<@gr(u?@gv=jA@g7-C@g	dD@g<ah\F@gG@g8!I@g	8K@gY/L@geOnN@gj^,P@)g|6*1@gYFi5@g<9@g'a	HE=@gs$']@@gB@g C@gocE@g7iG@gC2 WH@g.ai5JJ@gGiK@gS=M@gYz O@gJ6F
]P@)gpYDf2@g	W7@gnNUI:@gV/>@gA @@gK	i?B@g<bD@g1&F@g:>G@gwVI@g6&J@gL@gB85N@gIqrO@gF2P@)r~   r  r  r  r  r  r  r  r  r  r  r  r  r  r  )g:}u?gg$eS@g!@g~yyi'@gYJ(-@g'eN2@g$*5@g5O8@gMQ'Du;@g*S>@g2N@@gCqB@gGD@g'ǛE@gɏ(G@)r2   gV~@g^%^#@gM:W*@gy8X0@g|@N3@gYau6@g?+w9@g2JH<@gYv@L@@gVƇDA@g"s6C@g'D@gY{}v[F@gMxG@)gCKy@g:tg @g&@g{N+-@gQa1@g/?4@g%8@g_O;@gXWcx>@g.?@@gGOI|cB@gwpC@gd!E@gaG@gXqΰH@)g,E@g?>"@g+ x#])@g	p/@gH.23@gp]f6@g/}9@gݏ<@g|?D?@gO[E$MA@gN3!C@gY-:D@gA{I1JF@gBG@g?©mqI@)g"BV@gV4+
%@gp+@gCqP1@gӺoT4@g\7@gӉ;@g?3>@g9V@@g$0GB@gzC@gپ:rE@g=ςG@ggQ%H@gb0J@)g
K@g0uIx'@g#O.@gw/2@g5@g/9@gh<@gY-?@g9-BhA@g5;B@g!D@gԠP!-F@g{G@g-i
XI@gwDJ@)gȃ3/'!@ga)@gaȅ0@g^M3@g|D7@g͠8:@g0n=@g&_@@gswB@g<C@g`[FNE@g0ǡF@gAL|H@gnNfJ@gM 
K@)gzK#@g<VK%;,@g%1@g٣:5@g!R8@gVfF);@gw/{'?@g v2A@ge^B@g!KCjD@g`F@g.bG@gvWC4I@g"J@g?GӜaL@)gAl%@gsGϒ.@gQ@
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     5      (       d   e[        X5      R                  [        U    US-
     5      (       d   e[        XS5      R                  [        U    US-
     5      (       d   e[        XS5      R                  [        U    US-
     5      (       d   e[        X5      R                  [        U    US-
     5      (       d   e[        X5      R                  [        U    US-
     5      (       d   e[        XS5      R                  [        U    US-
     5      (       d   e[        XS5      R                  [        U    US-
     5      (       a  GM   e   GM     g )Nr   r   of)r   r   r(   VMprintr7   r   jn_small_zerosjnp_small_zerosr8   yn_small_zerosynp_small_zeros)rf   ms     r*   test_bessel_zeros_extrar  B	  s   BF1Xq1A!a#q#&&~a'81'=>>>>q#&&~a'81'=>>>>q1%(();AaC)@AAAAq1%(();AaC)@AAAAq#&&~a'81'=>>>>q#&&~a'81'=>>>>q1%(();AaC)@AAAAq1%(();AaC)@AAAA  r,   )9mathr  mpmathr+   r:   r>   rC   rG   rM   rg   r|   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r
  r  r  r  r  r"  r%  r,  r.  r1  r:  rD  rH  rl  rr  rv  ry  r  r  r  r  r  r  r  r  r  r  r  markslowr  r9   r,   r*   <module>r     s     IiV8M52
2,:x-^%.N
A!@bJH	Y	^e,3<8mt
DK,@,s.y.XT6Q>Z;(:<xAF"PAgF;=T~4>0@AF&C=N4J
(UT8< e` He` He` He` F B Br,   