
    h                         S SK Jr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  S SKJr  S SKJr  S SKJrJr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  S SK J!r!  S r"S r#S r$g)    )diffexpand_func)IRationalpi)S)Dummysymbols)catalan)	conjugate)sqrt)betabetaincbetainc_regularized)gamma	polygamma)hyper)Integral)ArgumentIndexError)	unchanged)raisesc            	      H  ^^ [        S5      u  mm[        S5      n [        [        TT5      (       d   e[        [        TT5      (       d   e[        SS5      R                  S:X  d   e[        ST5      R                  b   e[        [        TT5      5      [        T5      [        T5      -  [        TT-   5      -  :X  d   e[        [        TT5      [        TT5      -
  5      S:X  d   e[        [        TT5      5      [        [        TTS-   5      [        TS-   T5      -   5      R                  5       :X  d   e[        [        TT5      T5      [        TT5      [        ST5      [        STT-   5      -
  -  :X  d   e[        [        TT5      T5      [        TT5      [        ST5      [        STT-   5      -
  -  :X  d   e[        [        TT5      5      [        [        T5      [        T5      5      :X  d   e[        [        UU4S	 j5        [        TT5      R                  [        5      [        T5      [        T5      -  [        TT-   5      -  :X  d   e[        T5      R                  [        5      [        T5      S
-  [        S
T-  5      -  :X  d   e[        TT5      R                  [        5      R                  [        U TS-
  -  SU -
  TS-
  -  -  U SS45      5      (       d   e[        [!        SS5      [!        SS5      5      ["        R$                  :X  d   e[        [!        SS5      [!        SS5      5      SS
[#        S5      S-  -  -  ['        [(        5      -  [        ["        R*                  S-  5      -  S[        [#        S5      * S-  5      -  -  :X  d   e[        [!        SS5      [!        SS5      5      SS[-        [!        SS5      5      -  -  :X  d   e[        SS5      ["        R.                  :X  d   e[        SS5      ["        R.                  :X  d   e[        S
S5      ["        R*                  S-  :X  d   e[        [        TTS-   5      (       d   e[        [        TS5      (       d   e[        [        ST5      (       d   e[        TTS-   5      R1                  5       STTS-   -  [-        T5      -  -  :X  d   e[        ST5      R1                  5       ST-  :X  d   e[        TS5      R1                  5       ST-  :X  d   e[        [!        SS5      [!        SS5      SS9R1                  5       ["        R$                  :X  d   e[        S
5      [        S
S
5      :X  d   e[        TSS9[        TT5      :w  d   e[        TSS9R1                  5       [        TT5      :X  d   eg )Nzx yt   T   r      c                  :   > [        T T5      R                  S5      $ )Nr   )r   fdiff)xys   k/var/www/fran/franai/venv/lib/python3.13/site-packages/sympy/functions/special/tests/test_beta_functions.py<lambda>test_beta.<locals>.<lambda>$   s    tAqz'7'7':       i
   ii                  d   i'     F)evaluate)r
   r	   r   r   is_realr   r   simplifyr   r   r   r   r   rewriter   dummy_eqr   r   Zeror   r   Oner   ComplexInfinitydoit)r   r    r!   s    @@r"   	test_betar9      s   5>DAqc
AT1a    T1a    2;$&&&1:%%%tAqz"eAhuQx&7a!e&DDDDtAqzDAJ./1444tAqz"k$q!a%.4Aq>2Q&R&[&[&]]]]Q
A$q!*i1o	!QQRU@S.S"TTTTQ
A$q!*i1o	!QQRU@S.S"TTTTT!QZ D1y|$DDDD
:;1:e$aq(9%A,(FFFF7??5!U1Xq[qs%;;;;1:h'00!a!e*AQRUVQVGW:WZ[]^`aYb1cddddb!8B#34>>>b!8B#34A!QKR quuRx0#eQqTE!Gn2DEF F FR (2r"23sCQSUWHX@Y<Y7ZZZZ1:*****1:*****1:r!!!T1a!e$$$$T1a    T1a    1q5> Aq!A#wwqz'9$::::1:??!###1:??!###b!8B#3eDIIKqvvUUU7d1aj   E"d1aj000E"'')T!QZ777r%   c            
         [        S5      u  pp#[        [        XX#5      (       d   e[        [        XSU5      (       d   e[        SSSS5      R                  S:X  d   e[        SSSU5      R                  b   e[	        [        [
        SS[
        -
  SS[
        -  -   5      5      [        [
        * SS[
        -   SS[
        -  -
  5      :X  d   e[        XSS5      R                  [        5      R                  [        X5      R                  [        5      5      (       d   e[        SSSU5      R                  [        5      U[        S	S
U5      -  :X  d   e[        SSSS5      R                  5       S:X  d   eg )N	a b x1 x2r   r   r&   Tr   r)   r   r(   r&   )r
   r   r   r1   r   r   r3   r   r4   r   r   evalfabx1x2s       r"   test_betaincrE   <   sL   ;'LA"WaB++++WaAr****1aB''4///1aB''///WQ1q5!ac'23wr1a!eQQRSTQTW7UUUU1A&&x099$q*:L:LX:VWWWW1aB''."U7D"5M2MMMM1aA$$&!+++r%   c            
         [        S5      u  pp#[        [        XX#5      (       d   e[        [        XSU5      (       d   e[        SSSS5      R                  S:X  d   e[        SSSU5      R                  b   e[	        [        S[
        -  SS[
        -   SS[
        -  -   5      5      [        S	[
        -  SS[
        -
  SS[
        -  -
  5      :X  d   e[        XSS5      R                  [        5      S:X  d   e[        SSX#5      R                  [        5      SU-  [        S
SU5      -  SU-  [        S
SU5      -  -
  :X  d   e[        SSSS5      R                  5       S:X  d   eg )Nr;   r   r   r   r(   Tr   r&   r   r=   r>   r)   )
r
   r   r   r1   r   r   r3   r   r   r?   r@   s       r"   test_betainc_regularizedrG   L   si   ;'LA"(!7777(!26666q!Q+33t;;;q!Q+33;;;(1aQAaC@AEXY[\]Y]_`bcfgbgijmnopmpipEqqqqqQ*228<AAAq!R,44U;qtE'SWY[D\?\_`ac_cdijqswy{d|_|?||||q!Q*002a777r%   N)%sympy.core.functionr   r   sympy.core.numbersr   r   r   sympy.core.singletonr   sympy.core.symbolr	   r
   %sympy.functions.combinatorial.numbersr   $sympy.functions.elementary.complexesr   (sympy.functions.elementary.miscellaneousr   &sympy.functions.special.beta_functionsr   r   r   'sympy.functions.special.gamma_functionsr   r   sympy.functions.special.hyperr   sympy.integrals.integralsr   r   sympy.core.exprr   sympy.testing.pytestr   r9   rE   rG    r%   r"   <module>rV      sE    3 . . " . 9 : 9 W W D / . 2 % '(8V, 8r%   