
    \h6A                     X   S SK Jr  S SKJr  S SKJrJrJrJr  S SK	J
r
  S SKJr  S SKJrJr  S SKJr  S SKJr  S S	KJr  S S
KJrJrJr  S SKJr  S SKJrJrJr  S SK J!r!  S SK"J#r#J$r$  S SK%J&r'J(r)J*r+  S r,S r-S r.S r/S r0S r1S r2S r3S r4S r5\$S 5       r6\$S 5       r7S r8S r9S r:S r;g )!    )Tuple)
Derivative)IRationaloopi)S)symbols)explog)sqrt)cos)gamma)appellf1hypermeijerg)O)xzk)limit)raisesslow)random_complex_numberverify_numericallytest_derivative_numericallyc                  v    [        SS[        S-  5      n U R                  [        5      U S-  [        -  :X  d   eg )N    )r   r   diff)ps    `/var/www/auris/envauris/lib/python3.13/site-packages/sympy/functions/special/tests/test_hyper.pytest_TupleParametersBaser#      s2    b"adA66!9!A    c            	      p   [        [        S 5        [        SS[        5      [        [	        SS5      [	        S5      [        5      :X  d   e[        SS[        5      [        SS	[        5      :X  d   e[        SS[        S
S9n U R
                  [	        SSS5      :X  d   eU R                  [	        SSSS5      :X  d   e[        SS[        5      nUR
                  [	        SS5      :X  d   eUR                  [	        SSS5      :X  d   eUR                  [        :X  d   eUR                  SL d   e[        SS[        5      nUR
                  [	        SS5      :X  d   eUR                  [	        SSS5      :X  d   eUR                  [        :X  d   eUR                  SL d   e[        [        [	        5       [	        5       [        5      [        [        5      [        5      (       d   e[        [        [        S[	        S5      [        * 5      -  [        S[        -   5      [        5      (       d   e[        [        5       [        5       [        5       4[        5       [        5       4[        5      n[        U[        5      (       d   e[        S5      u  p#pEn[        X#4XEU4[        5      R                  [        5      X#-  XE-  U-  -  [        US-   US-   4US-   US-   US-   4[        5      -  :X  d   e[        [        // [        5      R                  [        5      [!        [        [        // [        5      [        5      :X  d   eSSKJn  [        U" [        5      /U" [&        5      /U" [(        5      5      [        [        /[&        /U" [(        5      5      :X  d   e[        SS[        S
S9R*                  [        L d   eg )Nc                  $    [        SS[        5      $ )N   r   )r   r   r   r$   r"   <lambda>test_hyper.<locals>.<lambda>   s    eAq!nr$   )r   r'   r'   r'   r   )r   r'   r   )r'   r   r'      r   r'   r+   Fevaluater+   r'   r   r+         r2   r3   T)r2   r+   r3   )r'   r'   z
a1:3, b1:4r   
polar_lift)r   	TypeErrorr   r   r   apbqargumentis_commutativetnr   r   randcplxtdr
   r    r   $sympy.functions.elementary.complexesr5   r   r   func)uha1a2b1b2b3r5   s           r"   
test_hyperrG      s   
9,-q!U5A;a!%DDDDL!,dFA0FFFFiq59A445Aq>!!!445Aq!$$$$fi#A445A;445Aq>!!!::??t###fi#A445A;445Aq>!!!::??t### eEGUWa(#a&!4444afeAh++SQZ;;;; 		XZ,xz8:.F	KAa88O8 .BBB"BB<+003
ruRx5"q&"q&!1BFBFBF3KQOOP P P !b!!!!$
5!b!3Da(HHHH @*Q-:a=/:a=AqcA3
1&' ' '
 q5166%???r$   c            	      @   SSK Jn JnJn  SSKJn  [        5       [        5       [        5       S-   penU" [        X/U/S5      5      [        U5      [        U * U-
  U-   5      -  [        U * U-   5      [        U* U-   5      -  -  :X  d   e[        U" [        XE/U/S5      5      R                  5       [        XE/U/S5      R                  5       -
  5      S:  d   eU" [        / / [        5      5      [        [        5      :X  d   eU" [        / SQ/ [        5      5      [        / SQ/ [        5      :X  d   eU" [        SS// /S/S//[        5      5      [        [        S-   5      :X  d   eU" [        SS// // / /[        5      5      [        SS// // / /[        5      :X  d   eg )Nr   )abc)expand_funcr3   r'   绽|=r'   r   r+   )	sympy.abcrI   rJ   rK   sympy.core.functionrL   r<   r   r   absnr   r   r   r   )rI   rJ   rK   rL   rB   rD   c1s          r"   test_expand_funcrT   I   s   !!/XZaBBuaVaS!,-arAvz""E1"q&M%Q-$?@A A A{5"B434668x"q)++-. /167 7 7 uRQ'(CF222uYA./5B3JJJJwA|qcA3Z;<AE
JJJwA|b"Xq9:!Qr2h*+ + +r$   c                     SSK Jn  U R                  U5      nU(       d  U $ [        U5      S:X  d   eU R	                  UR                  5       U05      $ )Nr   Dummyr'   )sympy.core.symbolrW   atomslenxreplacepop)exprsymrW   dums       r"   replace_dummyr`   [   sE    '
**U
Cs8q====#'')S)**r$   c                  j   SSK Jn   SSKJn  SSKJnJn  U" S5      n[        [        SS[        5      R                  U 5      U5      U " [        U-  U" U5      -  U" SU5      -  U" S	U5      -  US[        45      :X  d   e[        S
S[        5      R                  U 5      [        S
S[        5      :X  d   eg )Nr   )SumrV   )RisingFactorial	factorialr   r0   r-   r   r+   rN   )r+   )sympy.concrete.summationsrb   rX   rW   (sympy.functions.combinatorial.factorialsrc   rd   r`   r   r   rewriter   r   )rb   rW   rc   rd   _ks        r"   test_hyper_rewrite_sumrj   d   s    -'U	sBvvq199#>CArEIbM!OAr$::Ar"#%'BK	11 1 1 GQ'//4i!$% % %r$   c                      [        SS/[        5      R                  S:X  d   e[        SSS/[        5      R                  [        L d   e[        SS/[        5      R                  S:X  d   e[        SS/[        5      R                  [        L d   e[        SS	/[        5      R                  S:X  d   e[        S
S/[        5      R                  [        L d   e[        SSS/[        5      R                  S:X  d   e[        / SQSS/[        5      R                  S:X  d   e[        SS/SS/[        5      R                  [        L d   e[        / SQS/[        5      R                  S:X  d   e[        S/ [        5      R                  [        L d   e[        SS/S/S5      R                  S:X  d   e[        SS/S/S5      R                  S:X  d   e[        SS/S/S5      R                  S:X  d   e[        SS/S/S5      R                  S:X  d   eg )Nr0   r+   r'   r2   rN   r   )r   r'   r   )re   r'   r   )re   r   re   )re   r   rm   )re   r'   r+   r   )re   r   r+   r2   TF)r   r   radius_of_convergencer   convergence_statementr   r$   r"   test_radius_of_convergencerp   q   s   !a 66!;;;!Q#99R???QC#99Q>>>QC#99R???bT1%;;q@@@rdA&<<BBB2r(A&<<AAAb!Wa(>>!CCC"a2q'1%;;rAAAbT1%;;q@@@A&<<BBB!Q!a 66$>>>!Q!a 66%???!Q!b!774???!Q!b!775@@@r$   c                  N   [        [        S 5        [        [        S 5        [        SS[        5      [        [	        SS5      [	        S5      [	        S5      [	        S	5      [        5      :X  d   e[        S
SSS[        5      n U R
                  [	        SS5      :X  d   eU R                  [	        SSSSS	5      :X  d   eU R                  [	        SSS	5      :X  d   eU R                  [	        SSSS5      :X  d   eU R                  [	        SSSSSSSSS5	      :X  d   eU R                  [	        SSSSS5      :X  d   eU R                  [        :X  d   eU R                  S:X  d   eU R                  S:X  d   eU R                  SL d   eU R                  SL d   e[        / / /[         R"                  /S//S5      R                  SL d   e[        SS/S/S/S	/[        5      R                  [         R"                  :X  d   e[%        [        [	        5       [	        5       [	        S5      [	        5       [        * 5      ['        [        5      [        5      (       d   e[%        [)        [*        5      [        [	        5       [	        5       [	        S5      [	        [         R"                  5      [        S-  S-  5      -  [-        [        5      [        5      (       d   e[%        [        [	        SS5      [	        5       [	        S5      [	        S5      [        5      [/        S[        -   5      [        5      (       d   e[        [0        S 5        [        [0        S 5        [        [3        5       4[3        5       S[4        -  -   4[	        5       [3        5       [3        5       4[        5      n [7        U [        5      (       d   e[        [	        5       [3        5       4[	        5       [3        5       [3        5       4[        5      n [7        U [        5      (       d   e[        [	        5       [	        5       [	        [3        5       5      [	        [3        5       [3        5       5      [        5      n [7        U [        5      (       d   e[9        S5      u  pp4pVpx[        X4X44XV4Xx4[        5      R;                  [        5      [        US-
  U4X44XV4Xx4[        5      US-
  [        X4X44XV4Xx4[        5      -  -   [        -  :X  d   e[        [        [        // / / [        5      R;                  [        5      [=        [        [        [        // / / [        5      [        5      :X  d   eSSKJ n	  [        U	" U5      /U	" U5      /U	" U5      /U	" U5      /U	" [        5      5      [        U/U/U/U/U	" [        5      5      :X  d   eSS K!J"n
J#nJ$nJ%nJ&n  [        U
/U/U/U/[        5      RO                  U5      [        U-  [Q        X-
  5      -  [Q        U
* U-   S-   5      -  [Q        X-
  5      [Q        U* U-   S-   5      -  -  :X  d   eg )!Nc                  "    [        S[        5      $ )Nr'   r   r   r   r$   r"   r(   test_meijer.<locals>.<lambda>   s
    gamr$   c                  &    [        SSS[        5      $ )N)r*   r,   r+   r2   rs   r   r$   r"   r(   rt      s    glD$Br$   )r0   rv   )rw   )r3   r'   r   r+   r2   r3   r0   r1   )         	   )
               rx   ry   rz   r{   r|   r}   r~   r   r   K   re   TFr   c                  2    [        S[        4S4[        5      $ )N)r+   r'   r,   r   r   )r   r   r   r   r$   r"   r(   rt      s    w~vJr$   c                  $    [        SS[        5      $ )Nr   )r*   r   )r   r   r   r$   r"   r(   rt      s    w~~qIr$   za1:3, b1:3, c1:3, d1:3r4   )rI   rJ   rK   ds))r   r6   r   r   r   anr7   aotherbmr8   botherr9   nudeltar:   	is_numberr	   Halfr;   r   r   r   r   r   
ValueErrorr<   r   r=   r
   r    r   r>   r5   rO   rI   rJ   rK   r   r   	integrandr   )grB   rC   rD   rE   rS   c2d1d2plrI   rJ   rK   r   r   s                  r"   test_meijerr      s-   
9+,
9BC><3aU1XuQxq1=> > > 		<1EqIA445A;445Aq!Q''''88uQ1~%%%445Aq!$$$$445Aq!RRR888888uRRR0000::??442::77b==t###;;%Br7affXqcNA.88D@@@Aq6A3aS!,22aff<<< geguwa%'A2>AJJJJd2hwuw$Qxqvv1Q@ @ADQL L L LgeAqk57E!HeAhB!a%j!    :JK
:IJ 	
QqS 02EGXZ(!	-Aa88O8(*XZ(!	-Aa88O8%
"3hj(*-q	2Aa88O8%,-E%F"BBBBB8bXx"1=BB1E	"q&"x"B8Q	?FGRHrh2(AFF
GHI	JJ J J Aq62r2q)..q17Aq62r2q1156 6 6 FBrF8bfX2x"R&2a5ArdRD2$1./ / / ('A3aS1#q)33A6	1U15\%Q
++U15\%Q
:K-KLM M Mr$   c                     [        / SS/SS[        // [        5      R                  [        5      [	        [        5      [        / SS/SS[        // [        5      -  S[        / / SQSS[        S// [        5      -  -   :X  d   e[        5       n Sn[        [        [        // / / U 5      [        5      (       d   e[        [        [        S-  // / / U 5      [        5      (       d   e[        [        / [        // / U 5      [        5      (       d   e[        [        / / [        // U 5      [        5      (       d   e[        [        / / / [        /U 5      [        5      (       d   e[        [        [        /U/US-   // U 5      [        5      (       d   e[        [        [        /US-   /U// U 5      [        5      (       d   e[        [        [        U// / US-   /U 5      [        5      (       d   e[        [        [        US-   // / U/U 5      [        5      (       d   e[        SS5      n[        [        US-   /U/US-
  [        /U/U 5      [        5      (       d   eg )Nr'   r   r   )r'   r'   r'   r3   r+   )r   r   r   r    r   r<   r=   r   )yrI   rJ   s      r"   test_meijerg_derivativer      s   21v1ay"a055a8AwrAq6Aq!9b!44
GB	Aq!Q<Q7
7	88 8 8 	
A	Agqc2r2q)1----gq!tfb"b!,a0000gb1#r2q)1----gb"qc2q)1----gb"b1#q)1----gqcA3QQ/3333gqcAE7QCQ/3333gq!fb"q1ugq115555gq!a%j"b1#q115555AAgq1ugsQUAJQ7;;;;r$   c                  v   [        / S/S// [        5      R                  5       S[        -  :X  d   e[        S// / S/[        5      R                  5       S[        -  :X  d   e[        / / S// [        5      R                  5       S[        -  :X  d   e[        / / S/[        R
                  /[        5      R                  5       S[        -  :X  d   e[        / / [        R
                  /S/[        5      R                  5       S[        -  :X  d   e[        SS// S/S/[        5      R                  5       [        L d   eg )Nr'   r   r   r2   )r   r   
get_periodr   r	   r   r   r   r$   r"   test_meijerg_periodr      s   2sQCQ'224"<<<A3BQ'224"<<<2rA3A&113qt;;;
BaffXq"",*,!B$7 7 7
B1#q"",*,!B$7 7 7Aq62sQC+668B>>>r$   c                     SSK Jn   U " S[        -  [        -  5      [        -  n[        n[        / / U5      R                  U:X  d   e[        S// U5      R                  U:X  d   e[        S/S/U5      R                  U:X  d   e[        SS/S/U5      R                  U:X  d   e[        SS/S/U " S[        -  [        -  5      5      R                  S:X  d   eg )Nr   	exp_polarr   r'   )&sympy.functions.elementary.exponentialr   r   r   r   r   r9   )r   rI   rJ   s      r"   test_hyper_unpolarifyr      s    @!B$q&!A	AR$$)))!b!%%***!qc1&&!+++!Q!a ))Q...!Q!i"Q/099Q>>>r$   c                  	  ^^^^^ SSK Jn JnJnJnJnJnJnJnJ	nJ
n	Jn
Jn  SSKJm  SSKJn  [#        S5      u  mmmmn " UUUU4S jSU 5      nU" U5      R%                  S5      U" S['        U5      S	:  4TS
45      :X  d   eU" T" [(        [*        -  5      U-  5      R%                  S5      U" S['        U5      S	:  4TS
45      :X  d   eU" T" S[(        -  [*        -  5      U-  5      R%                  S5      U" T['        U5      S	:  4TS
45      :X  d   eU" T" S[(        -  [*        -  5      U-  5      R%                  S5      U" T['        U5      S	:  4TS
45      :X  d   eU" T" S[(        -  [*        -  5      U-  5      R%                  S5      U" ST-  ['        U5      S	:  4TS
45      :X  d   eU" T" S[(        -  [*        -  5      U-  5      R%                  S5      U" ST-  ['        U5      S	:  4TS
45      :X  d   eU" U5      R%                  S5      T:X  d   eU" T" [(        [*        -  5      U-  5      R%                  S5      T:X  d   eU4S jn[-        S	S5      mU" U" U5      [/        [0        R2                  S	/[-        SS5      /U5      U5      (       d   eU" U" TU5      [/        T* // U5      U5      (       d   eU" U" TU5      [/        TT[0        R2                  -
  /ST-  /U5      U5      (       d   eU" U" U5      U* [/        S	S	/S/U5      -  U5      (       d   eU" U" U5      [/        [0        R2                  [0        R2                  /[-        SS5      /U5      U5      (       d   eU" U" U5      [/        S	S	/[-        SS5      /U5      U5      (       d   eU" U" TU5      [/        T* [0        R2                  T-
  /[0        R2                  /U5      U5      (       d   eU" U" TU5      SU-  ST-  S	-   -  [/        T* [0        R2                  -
  T* /[0        R2                  /U5      R5                  U5      -  U5      (       d   eU" U	" U5      U* S-  [/        [-        SS5      S	S	/SS/U5      -  U5      (       d   eU" U
" TU5      [/        T* T/[0        R2                  /U5      U5      (       d   eU" U" TU5      ST-  U-  [/        S	T-
  S	T-   /[-        SS5      /U5      -  U5      (       d   eg )Nr   )HyperRepHyperRep_atanhHyperRep_power1HyperRep_power2HyperRep_log1HyperRep_asin1HyperRep_asin2HyperRep_sqrts1HyperRep_sqrts2HyperRep_log2HyperRep_cosasinHyperRep_sinasinr   )	Piecewisez	a b c d zc                   n   > \ rS rSr\U 4S j5       r\U4S j5       r\U4S j5       r\U4S j5       rSr	g)test_hyperrep.<locals>.myrep   c                    > T$ Nr   )clsr   rI   s     r"   _expr_small(test_hyperrep.<locals>.myrep._expr_small       Hr$   c                    > T$ r   r   )r   r   rJ   s     r"   _expr_small_minus.test_hyperrep.<locals>.myrep._expr_small_minus  r   r$   c                    > TU-  $ r   r   )r   r   rR   rK   s      r"   	_expr_big&test_hyperrep.<locals>.myrep._expr_big      Q3Jr$   c                    > TU-  $ r   r   )r   r   rR   r   s      r"   _expr_big_minus,test_hyperrep.<locals>.myrep._expr_big_minus	  r   r$   r   N)
__name__
__module____qualname____firstlineno__classmethodr   r   r   r   __static_attributes__rI   rJ   rK   r   s   r"   myrepr      sQ    		 
	 
	 
	 
	 
	 
	 
	r$   r   nonrepr'   Tr   r+   r2   r3   nonrepsmallc           
      ,  >^ [        U R                  S5      UT[        SS5      [        SS5      [        R                  [        R                  S9(       d  g[        U R                  S5      R                  TT" [        [        -  5      T-  5      R                  T[        5      U R                  TT" [        [        -  5      T-  5      R                  S5      T[        SS5      [        SS5      [        R                  [        R                  S9(       d  gU R                  TT" [        [        -  5      T-  5      R                  S5      n[        UR                  TS5      R                  5       UR                  TS5      R                  5       -
  5      S	:  a  gUU4S
 jnS H  nU" U S[        -  [        -  U-  [        [        -  S-  5      nU" U S[        -  [        -  U-  [        [        -  -   [        * [        -  S-  5      n[        XgT5      (       d    gU" U S[        -  [        -  US-   -  [        * [        -  S-  5      nU" U S[        -  [        -  U-  [        [        -  -   [        [        -  S-  5      n[        XgT5      (       a  M    g   g)z1Test that func is a valid representation of hyp. r   re   r   r   Fr   g     ?g?rM   c                    > U R                  TT" U5      T-  5      R                  S5      nUR                  TT" U5      T-  5      R                  T[        5      $ )Nr   )subsrh   replacer   )r?   rI   rJ   rvr   r   s       r"   dosubs(test_hyperrep.<locals>.t.<locals>.dosubs-  sL    1il1n-55h?B771il1n-55iEEr$   )	r   r'   r   r+   r2   re   rm   rl   r'   T)r;   rh   r   r	   r   r   r   r   r   r   rQ   rR   )	r?   hypr   r]   r   rR   expr1expr2r   s	     `     r"   ttest_hyperrep.<locals>.t  s    $,,}-sAROxA!&&AFFLLL',,9QrT?1$&&-gi&=IIa1R4*+33MBXb!_Q166QVV	M
 yyIadOA-.66x@tyyI&((*TYYq)-D-F-F-HHIEQ	F 1A41R1R462E41RAbD1"R%':EeA&&41RQ!Bq9E41RAbD!B$q&9EeA&& 1 r$   rm   )sympy.functions.special.hyperr   r   r   r   r   r   r   r   r   r   r   r   r   r   $sympy.functions.elementary.piecewiser   r
   rh   rQ   r   r   r   r   r	   r   r    )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rI   rJ   rK   r   r   s                   @@@@@r"   test_hyperrepr      s   , , , ,
 A>K(MAq!Q    8H%As1vz?QI)NNNN1R4"#++H51c!fqj/At9-. . .1Q3r6"1$%--h71c!fqj/At9-. . .1Q3r6"1$%--h71c!fqj/At9-. . .1Q3r6"1$%--h71Q3A
#aY/0 0 01Q3r6"1$%--h71Q3A
#aY/0 0 08M*a///1R4"#++M:a???D 	AA^AqvvqkHQN3CQ GKKKK_Q"EA2$A$6::::_Q"E1a!&&j/AaC5!$DaHHHH]1r%AQ"77;;;;^Aqvvqvv&6!Q8H! LaPPPP^Aq!fx1~.> BAFFFF_Q"EA2qvvz*:QVVHa$H!LLLL_Q"T1Q37^EA2;"3affXqAFFqII1N N N N]1r!tE8Aq>1a*@1a&!$LLaPPPPa#UQB7QVVHa%@!DDDDa#QqSU5!a%Q(1a.AQST+U%UWXYYYYr$   c                  $   SSK Jn   SSKJn  SSKJn  [        5       n[        U " [        [        -  [        -  5      -  n[        [        / US-   S-  //US-  /U* S-  US-   S-  //US-  S-  5      -  nU" X45      nS He  nS	 H\  n[        XV-
  R                  [        U[        U0S
95      S:  d   e[        XV-
  R                  [        U[        U* 0S
95      S:  a  M\   e   Mg     Sn	UR                  [        U5      nS H  nS[        SS5      SS[        SS5      SS4 Hj  n[        XV-
  R                  [        U[        X-   X(U	-
  0S
95      S:  d   e[        XV-
  R                  [        U[        U* U	-   X(* U	-
  0S
95      S:  a  Mj   e   M     [        SSU " [        * [        -  5      S-  5      [        SSU " [        [        -  5      S-  5      -   S[!        [        5      -  -  n
U
[        [#        S5      -  -
  R                  SS9S:X  d   eg )Nr   r   )besseli)lr'   r   r2   )      ?      ?)g        g?g333333?r   g?r'   g/$@g.@)r   rM   gvIh%<=r   r+   g      ?g      ?g      ?r   ))r   r   ))r   r   r   r   T)chop)r   r   sympy.functions.special.besselr   rO   r   r<   r   r   r   r   r   rQ   rR   r   r   r   r   )r   r   r   rI   argr   r   x_k_epsr]   s              r"   test_meijerg_evalr   K  s>   @6
A
Iad1f
Cwa!eQYK(AaC5A2a4!a%2C*Dc1fQhOOEAOE ;B((q"an(=>FFF((q"a"o(>?%GGG <  CJJq!EAdHQNCMB((ArxH= ) ? @BGH H H((AsSy!S3Y? ) A BDIJ J J N  L"5y!B7G7IJl$71R49JKL
DH*D 2c!f9T*a///r$   c                  $   [        S5      u  p[        S[        SS5      [        SS5      4U S-  5      R                  U 5      SSU S-  -  S	-  -   S
U S-  -  S-  -   [	        U S-  5      -   :X  d   e[        S[        SSU5      -  US5      S:X  d   eg )Nzk, xr*   r2   r+   r3   r   r'   r{      Q   i`  rx   r   )r
   r   r   seriesr   r   )r   r   s     r"   test_limitsr   k  s    6?DAAA7A>EEaHqAvby=2ad74<'!AqD'12 2 2 5q))1a0A555r$   c            
         [        S5      u  pp#pE[        XXXT5      [        XX#XE5      :X  d   e[        XXXT5      [        XXXE5      :X  d   e[        XX#[        R                  [        R                  5      [        R                  L d   e[        XX#[        R                  [        R                  SS9nUR
                  [        L d   eUR                  5       [        R                  L d   eg )Nza b1 b2 c x yFr.   )r
   r   r	   ZeroOner?   doit)rI   rD   rE   rK   r   r   fs          r"   test_appellf1r   t  s     1A2!A2!'8A2!+GGGGA2!'8A2!+GGGGA2!&&!&&1QUU:::qvvqvv>A66X668quur$   c                     SSK Jn   [        S5      u  pp4pVnU " [        XX4XV5      U5      X-  [        US-   X2S-   US-   Xe5      -  U-  :X  d   eU " [        XX4XV5      U5      X-  [        US-   X#S-   US-   XV5      -  U-  :X  d   eU " [        XX4XV5      U5      S:X  d   eU " [        XX4XV5      U5      [	        [        XX4XV5      U5      :X  d   eg )Nr   )r    za b1 b2 c x y zr'   )rP   r    r
   r   r   )r    rI   rD   rE   rK   r   r   r   s           r"   test_derivative_appellf1r     s    (#$56A2!q,a0AD!a%RSVUVYZUZ\]9a4abc4ccccq,a0AD!a%RSVUVYZUZ\]9a4abc4ccccq,a0A555q,a0ZPRWX@\^_5````r$   c                  H   [        S5      u  pp#[        SS[        S-  5      R                  [        SS 5      S[        S-  S-  -   [        S-  S	-  -   [        S
-  S-  -   [	        [        S-  5      -   :X  d   e[        [        5      R                  [        SS 5      [        X4X4[        5      R                  [        SS 5      :X  d   e[        X4X4[        5      R                  [        SS 5      [        X4X4[        5      [	        [        S-  5      -   :X  d   e[        [        S5      * S-  [        S5      S-  4SS[        -  [        S-   -  5      R                  [        5      S[        -
  [        S-  S-  -   S[        S-  -  S-  -
  S[        S-  -  S-  -
  S[        S-  -  S-  -
  [	        [        S
-  5      -   :X  d   e[        S-  [        [        S5      * S-  [        S5      S-  4SS[        -  [        S-   -  5      -  R                  [        5      [        S-  [        [        -  S-  -
  [        [        S-  -  S-  -   S[        -  [        S-  -  S-  -
  S[        -  [        S-  -  S-  -
  S[        -  [        S-  -  S-  -
  [	        [        S
-  5      -   :X  d   eg )Nza1 b1 a2 b2r0   rN   r   ry   r'   r+   r2      rx   ih  r*      @   ]   r3   rz      )
r
   r   r   _eval_nseriesr   r   r   r	   nseriesr   )rB   rD   rC   rE   s       r"   test_eval_nseriesr     sl   ]+NBBA&44Q4@	AqDF
QT"Wq!tCx'!AqD'12 2 2q6!D)rh!$221a>? ? ?"B8Q'55aDArh!$qAw./ / /1Q4%'1Q46"D!A#q1u+6>>qA	A1Q1a4!Bq!tGBJ.AqD;a1gEF F FqD1a1a($!QU<<EEaH
1r!tAv1a4	!AbDAIaK/"R%1*S.@2b5A:c>QTUVWYZVZT[[\ \ \r$   N)<sympy.core.containersr   rP   r   sympy.core.numbersr   r   r   r   sympy.core.singletonr	   rX   r
   r   r   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr   'sympy.functions.special.gamma_functionsr   r   r   r   r   sympy.series.orderr   rO   r   r   r   sympy.series.limitsr   sympy.testing.pytestr   r   sympy.core.randomr   r<   r   r;   r   r=   r#   rG   rT   r`   rj   rp   r   r   r   r   r   r   r   r   r   r   r   r$   r"   <module>r
     s    ' * 4 4 " % = 9 8 9 D D     % -' '+@\+$+
%A&@MF<(?? VZ VZr 0 0>6a\r$   