U
    L?hiL  ã                   @   s„  d dl mZ d dlmZmZ d dlmZmZmZm	Z	 d dl
mZ d dlmZmZ d dlmZmZmZ d dlmZ d dlmZ d d	lmZ d d
lmZ d dlmZ d dlmZ d dlm Z  d dl!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4 d dlm5Z5 d dl6m7Z7 edƒZ8dd„ Z9dd„ Z:dd„ Z;dd„ Z<dd„ Z=dd „ Z>d!d"„ Z?d#d$„ Z@d%d&„ ZAd'S )(é    )ÚSum)Ú
DerivativeÚdiff)ÚRationalÚooÚpiÚzoo)ÚS)ÚDummyÚSymbol)ÚRisingFactorialÚbinomialÚ	factorial)Ú	conjugate)Úexp)Úfloor)Úsqrt)Úcos)Úgamma)Úhyper)Úassoc_laguerreÚassoc_legendreÚ
chebyshevtÚchebyshevt_rootÚ
chebyshevuÚchebyshevu_rootÚ
gegenbauerÚhermiteÚhermite_probÚjacobiÚjacobi_normalizedÚlaguerreÚlegendre)Úlaguerre_poly)Úroots)Ú	unchanged)ÚArgumentIndexError)ÚraisesÚxc               
      s@  t dƒ‰t dƒ‰ t dƒ‰tdˆ ˆtƒdks.t‚tdˆ ˆtƒˆ d ˆd  tˆ d ˆd  d   ksht‚tˆˆ ˆ tƒtˆ d ˆƒtˆˆ tj tƒ tdˆ  d ˆƒ ks¬t‚tˆˆ ˆ  tƒdˆ  t d ˆ  d   td ˆ d   tˆˆ tƒ t	ˆ  ˆ ƒ t
ˆ ˆ d ƒ t	ˆ ˆ ƒt
ˆd ƒ  ks0t‚tˆˆ ˆtƒt d ˆd  td ˆ d   tˆˆtƒ t
ˆ ˆ d ƒ t
ˆd ƒ ks”t‚tˆddtƒtˆtƒks²t‚tˆtjtjtƒttddƒˆƒtˆtƒ t	ˆd ƒ ksðt‚tˆtddƒtddƒtƒttjˆƒtˆtƒ t	ˆƒ ks.t‚tˆˆ ˆtƒ} t| tƒsLt‚tˆˆ ˆt ƒdˆ tˆˆˆ tƒ ksxt‚tˆˆ ˆdƒdˆ  t
ˆ ˆ d ƒ tˆ ˆ ˆ fˆ d fdƒ t	ˆƒt
ˆ d ƒ  ksØt‚tˆˆ ˆdƒtˆ d ˆƒt	ˆƒ kst‚t d	d
d}t|ˆ ˆtƒttˆ ˆ | d |ƒ ks<t‚ttˆˆ ˆtƒsRt‚tt|ˆ ˆtƒƒt|tˆ ƒtˆƒttƒƒks„t‚tdƒ}ttˆˆ ˆtƒˆƒttˆˆ ˆtƒˆƒksºt‚ttˆˆ ˆtƒˆ ƒ ttˆˆ ˆtƒd| ˆ  ˆ d t|ˆ d | ˆ ƒ t|ˆ ˆtƒ | ˆ t|ˆ  ˆ d | ˆ ƒ   |ˆ  ˆ ˆ d  |dˆd fƒ¡sht‚ttˆˆ ˆtƒˆƒ td| ˆ  d| ˆ  ˆ d  t|ˆ  d | ˆ ƒ t|ˆ ˆtƒ | ˆ t|ˆ  ˆ d | ˆ ƒ  tˆˆ ˆtƒ |ˆ  ˆ ˆ d  |dˆd fƒ¡s$t‚ttˆˆ ˆtƒtƒˆ d ˆd  ˆd  tj tˆd ˆ d ˆd tƒ ksvt‚tˆˆ ˆtƒtˆˆ ˆtƒtdˆ ˆ d  t
ˆ ˆ d ƒ t
ˆˆ d ƒ ˆ ˆ dˆ  d t	ˆƒ t
ˆ ˆ ˆ d ƒ  ƒ ksüt‚tt‡ ‡fdd„ƒ ttdd„ ƒ tˆˆ ˆtƒ t¡ ttjtd  | tˆ |ƒ t|ˆ  d | ˆ ƒ tˆ ˆ ˆ d |ƒ t	|ƒ |dˆfƒt	ˆƒ ¡s¢t‚tˆˆ ˆtƒ d¡ ttjtd  | tˆ |ƒ t|ˆ  d | ˆ ƒ tˆ ˆ ˆ d |ƒ t	|ƒ |dˆfƒt	ˆƒ ¡s&t‚tt‡ ‡‡fdd„ƒ d S )NÚnÚaÚbr   é   é   éÿÿÿÿé   ÚmT©ÚpositiveÚkc                      s   t dˆ ˆtƒS ©NgÍÌÌÌÌÌ À)r   r(   © )r*   r+   r5   úe/var/www/html/venv/lib/python3.8/site-packages/sympy/functions/special/tests/test_spec_polynomials.pyÚ<lambda>N   ó    ztest_jacobi.<locals>.<lambda>c                   S   s   t tdddddtƒS )NT)r2   Úintegerr,   r-   )r   r
   r   r5   r5   r5   r6   r7   O   r8   Ú
polynomialc                      s   t ˆˆ ˆtƒ d¡S )Né   )r   r(   Úfdiffr5   ©r*   r+   r)   r5   r6   r7   W   r8   )r   r   r(   ÚAssertionErrorr   r   r	   ÚHalfr   r   r   r"   r   r   r   Ú
isinstancer   r   r%   r   r
   r   r   Údummy_eqr   r    r   r'   Ú
ValueErrorÚrewriter&   ©ÚXr0   Ú_kr5   r=   r6   Útest_jacobi   s   : ÿÿÿ
Dÿÿÿ<ÿ
ÿ ÿÿ
ÿ ÿÿÿ,&  ÿÿ*.ÿ
."0 ÿ$ÿÿÿÿÿþý(ÿÿÿÿÿ$þ ÿþýý6ÿ
<.ÿÿ
"ÿ
ÿÿþþþþ"ÿ
ÿÿþþþþrG   c               	      s   t dƒ‰t dƒ‰ tdˆ tƒdks$t‚tdˆ tƒdˆ  t ks@t‚tdˆ tƒˆ  td dˆ d  dˆ     ksrt‚tdˆ tƒtd dˆ d  d dˆ d   ˆ tddƒ   td	ˆ d  dˆ     ksÌt‚td
ˆ tƒdksàt‚tˆtjtƒtˆtƒksüt‚tˆdtƒtˆtƒkst‚tˆd
tƒdks.t‚tˆˆ tƒ} t	| tƒsJt‚tˆˆ t ƒd
ˆ tˆˆ tƒ ksrt‚tˆˆ dƒdˆ t
tƒ tˆ ˆd  ƒ tˆ ƒtˆ d tj ƒ tˆd ƒ  ksÌt‚tˆˆ dƒtdˆ  ˆ ƒtdˆ  ƒtˆd ƒ  kst‚tˆtddƒd
ƒtks"t‚tˆtddƒd
ƒt
dƒttˆtjd   ƒ tˆtj ƒ t
tƒtˆd ƒ  kszt‚t ddd}t|ˆ tƒttˆ |ƒ ks¦t‚ttˆˆ tƒsºt‚ttˆˆ tƒƒtˆtˆ ƒttƒƒksät‚tdƒ}ttˆˆ tƒˆƒttˆˆ tƒˆƒkst‚ttˆˆ tƒˆ ƒ tdd
| ˆ   d |ˆ   t|ˆ tƒ | ˆ |dˆ   ˆ   d| d |dˆ   d| dˆ   d   d|dˆ   ˆ   tˆˆ tƒ  |dˆd fƒ¡sÐt‚ttˆˆ tƒtƒdˆ  tˆd ˆ d tƒ kst‚tˆˆ tƒ t¡ td
| dt d	| ˆ   tˆ | ˆ ƒ t|ƒtd	| ˆ ƒ  |dtˆd ƒfƒ¡svt‚tˆˆ tƒ d¡ td
| dt d	| ˆ   tˆ | ˆ ƒ t|ƒtd	| ˆ ƒ  |dtˆd ƒfƒ¡sèt‚tt‡ ‡fdd„ƒ d S )Nr)   r*   r   r,   r-   r/   é   é   éþÿÿÿr.   r0   Tr1   r3   r:   c                      s   t ˆˆ tƒ d¡S ©NrH   )r   r(   r<   r5   ©r*   r)   r5   r6   r7   ‹   r8   z!test_gegenbauer.<locals>.<lambda>)r   r   r(   r>   r   r	   r?   r"   r   r@   r   r   r   r   r   ZOner   r   r%   r   r
   r   r   rA   r   rC   r   r   r'   r&   rD   r5   rL   r6   Útest_gegenbauerZ   sŒ    2
Hÿ(ÿ&ÿ:,ÿÿ **(ÿ
ÿÿÿÿÿÿÿÿý4,ÿÿÿ
,ÿÿÿ
rM   c                     sú  t dtƒdkst‚t dtƒtks$t‚t dtƒdtd  d d  ¡ ksJt‚t dtƒdtd  dt  d  ¡ kstt‚t dtƒdtd  dtd   d d	  ¡ ks¦t‚t dtƒd
td  dtd   dt  d	  ¡ ksÜt‚t dtƒdtd  dtd   dtd   d d  ¡ kst‚t ddƒdks0t‚t ddƒdksDt‚t ddƒdksXt‚t ddƒdkslt‚t ddƒdks€t‚t ddƒdks”t‚t dtƒdks¨t‚tdƒ} t d|  tƒ | d¡dtd  dt  d  ¡ ksèt‚tt dtƒtƒttddƒtddƒtdƒ  ƒdttddƒtddƒtdƒ  ƒ dttddƒtddƒtdƒ  ƒdttddƒtddƒtdƒ  ƒ diks†t‚tdƒ‰ t ˆ tƒ}t	|t ƒs¨t‚t
t ˆ tƒsºt‚t ˆ dƒttƒttjˆ d  ƒtˆ d d ƒ  ksôt‚t ˆ dƒdkst‚t ˆ tƒtkst‚t ˆ  tƒt ˆ d tƒks<t‚t ˆ t ƒdˆ  t ˆ tƒ ks`t‚t
t ˆ  |  tƒsxt‚tt ˆ tƒƒt ˆ ttƒƒksšt‚tt ˆ tƒtƒˆ tt ˆ tƒ t ˆ d tƒ  td d  ksÜt‚tt ˆ tƒˆ ƒtt ˆ tƒˆ ƒkst‚tdƒ}t ˆ tƒ t¡ td| tjtd  |  td tj | ˆ    tˆ |ƒd  |dˆ fƒ¡snt‚t ˆ tƒ d¡ td| tjtd  |  td tj | ˆ    tˆ |ƒd  |dˆ fƒ¡sÒt‚tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nr   r,   r-   r/   r;   rH   é#   é   rI   é?   éF   é   é   éç   i;  éi   é   é
   r.   é   r3   é   r)   r:   c                      s   t ˆ tƒ d¡S ©Nr,   ©r"   r(   r<   r5   ©r)   r5   r6   r7   Á   r8   ztest_legendre.<locals>.<lambda>c                      s   t ˆ tƒ d¡S ©Nr/   r[   r5   r\   r5   r6   r7   Â   r8   )r"   r(   r>   Úexpandr   Úsubsr$   r   r   r@   r%   r   r   r	   r?   r   r   r   r   r
   rC   r   rA   r   r'   r&   )r3   rE   rF   r5   r\   r6   Útest_legendreŽ   s„    &*26@8      ü
: $"*ÿ
&ÿÿÿÿÿÿÿÿÿÿr`   c                     s  t ‰ tdtd  ƒ} ˆ ddtƒdks(t‚ˆ ddtƒtks<t‚ˆ ddtƒ|  ksRt‚ˆ ddtƒdtd  d d ksvt‚ˆ ddtƒdt |  ks’t‚ˆ ddtƒd| d  ks®t‚ˆ ddtƒdtd  dt  d ksÖt‚ˆ ddtƒ ¡ dddtd    d  ¡ |   ¡ kst‚ˆ ddtƒdt | d  ks2t‚ˆ ddtƒd| d  ksPt‚ˆ dd	tƒˆ ddtƒ d kstt‚ˆ dd
tƒˆ ddtƒd ks–t‚ˆ dd	tƒˆ ddtƒ d ksºt‚ˆ ddtƒˆ ddtƒ d ksÞt‚ˆ dd
tƒˆ ddtƒd ks t‚ˆ dd	tƒˆ ddtƒ d ks$t‚tdƒ‰tdƒ‰ˆ ˆˆtƒ}t|t ƒsPt‚ˆ ˆdtƒtˆtƒkslt‚ˆ ˆˆdƒdˆ ttƒ t	ˆ d ˆd  t
j ƒt	ˆ d ˆd  d ƒ  ksÄt‚tˆ ˆˆtƒtƒˆt t ˆˆtƒ ˆˆ t ˆd ˆtƒ  td d  kst‚tdƒ}ˆ ˆˆtƒ t¡ dtd  ˆd  td	| dˆ   td
| ˆ ˆ   td
| dˆ  ƒ t|ƒt| ˆ ƒ td
| ˆ ˆ ƒ  |dtˆd ˆd  ƒfƒ ¡sÊt‚ˆ ˆˆtƒ d¡ dtd  ˆd  td	| dˆ   td
| ˆ ˆ   td
| dˆ  ƒ t|ƒt| ˆ ƒ td
| ˆ ˆ ƒ  |dtˆd ˆd  ƒfƒ ¡sxt‚tt ˆˆtƒƒt ˆtˆƒttƒƒks¢t‚tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ ‡‡fdd„ƒ tt‡ ‡‡fdd„ƒ tt‡ ‡‡fdd„ƒ d S )Nr,   r-   r   r/   éýÿÿÿr;   rR   iñÿÿÿr.   rJ   é   rS   éÐ  éx   é   r)   r0   r3   r:   c                      s   ˆ ddt ƒS )Nr   r,   ©r(   r5   ©ÚPlmr5   r6   r7   ó   r8   z%test_assoc_legendre.<locals>.<lambda>c                      s   ˆ ddt ƒS )Nr.   r,   rf   r5   rg   r5   r6   r7   ô   r8   c                      s   ˆ ˆˆt ƒ d¡S rZ   ©r(   r<   r5   ©rh   r0   r)   r5   r6   r7   õ   r8   c                      s   ˆ ˆˆt ƒ d¡S )Nr-   ri   r5   rj   r5   r6   r7   ö   r8   c                      s   ˆ ˆˆt ƒ d¡S rK   ri   r5   rj   r5   r6   r7   ÷   r8   )r   r   r(   r>   r^   r   r@   r"   r   r   r	   r?   r   r
   rC   r   rA   r   r   r   r'   rB   r&   )ÚQrE   rF   r5   rj   r6   Útest_assoc_legendreÅ   s€    $(:"$"$$"$*ÿÿ"ÿ
ÿ:ÿ ÿÿþÿ
:ÿ ÿÿþÿ
ÿ
rl   c               	      s  t dtƒdkst‚t dtƒtks$t‚t dtƒdtd  d ksBt‚t dtƒdtd  dt  ksdt‚tddƒD ]@‰ tˆ ƒD ] } tˆ | ƒ}t ˆ |ƒdkszt‚qztt‡ fdd„ƒ qntddƒD ]@‰ tˆ ƒD ] } tˆ | ƒ}tˆ |ƒdksÆt‚qÆtt‡ fdd„ƒ qºt	d	ƒ‰ t ˆ tƒ}t
|t ƒst‚tt ˆ tƒs0t‚t ˆ t ƒd
ˆ  t ˆ tƒ ksTt‚t ˆ  tƒt ˆ tƒkspt‚t ˆ dƒttˆ  d ƒkst‚t ˆ dƒdks¤t‚t ˆ tƒtks¸t‚tt ˆ tƒƒt ˆ ttƒƒksÚt‚tt ˆ tƒtƒˆ tˆ d tƒ kst‚tˆ tƒ}t
|tƒst‚t	dƒ}tˆ t ƒd
ˆ  tˆ tƒ ksHt‚tˆ  tƒtˆ d tƒ ksjt‚ttˆ  | tƒs‚t‚tˆ dƒttˆ  d ƒks¢t‚tˆ dƒˆ d ksºt‚tˆ tƒtksÎt‚ttˆ tƒƒtˆ ttƒƒksðt‚ttˆ tƒtƒt tˆ tƒ ˆ d t ˆ d tƒ  td d  ks8t‚tdƒ}t ˆ tƒ t¡ ttd| ˆ   td d |  tˆ d| ƒ |dtˆ d ƒfƒ¡sšt‚t ˆ tƒ d¡ ttd| ˆ   td d |  tˆ d| ƒ |dtˆ d ƒfƒ¡sôt‚tˆ tƒ t¡ td
| dt d| ˆ    t| ˆ  ƒ t|ƒtd| ˆ  ƒ  |dtˆ d ƒfƒ¡sbt‚tˆ tƒ d¡ td
| dt d| ˆ    t| ˆ  ƒ t|ƒtd| ˆ  ƒ  |dtˆ d ƒfƒ¡sÐt‚tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nr   r,   r-   r/   rH   c                      s
   t ˆ ˆ ƒS ©N)r   r5   r\   r5   r6   r7     r8   z test_chebyshev.<locals>.<lambda>c                      s
   t ˆ ˆ ƒS rm   )r   r5   r\   r5   r6   r7   
  r8   r)   r.   Úyr3   rJ   r:   c                      s   t ˆ tƒ d¡S rZ   ©r   r(   r<   r5   r\   r5   r6   r7   7  r8   c                      s   t ˆ tƒ d¡S r]   ro   r5   r\   r5   r6   r7   8  r8   c                      s   t ˆ tƒ d¡S rZ   ©r   r(   r<   r5   r\   r5   r6   r7   9  r8   c                      s   t ˆ tƒ d¡S r]   rp   r5   r\   r5   r6   r7   :  r8   )r   r(   r>   Úranger   r'   rB   r   r   r   r@   r%   r   r   r   r   r   r
   rC   r   rA   r   r   r   r&   )r3   ÚzrE   rn   rF   r5   r\   r6   Útest_chebyshevú   sž    "


$ "(
$" "0ÿ
 ÿÿÿ ÿÿÿ
ÿÿÿÿþ
ÿÿÿÿþrs   c               
      sô  t dtƒdkst‚t dtƒdt ks(t‚t dtƒdtd  d ksFt‚t dtƒdtd  dt  ksht‚t dtƒdtd  d	td   d ks’t‚t d
tƒdtd
  dtd   dtd   d ksÈt‚tdƒ‰ tt ˆ tƒsàt‚t ˆ t ƒdˆ  t ˆ tƒ kst‚tt ˆ  tƒst‚t ˆ dƒdˆ  ttƒ ttj	ˆ d  ƒ ksJt‚t ˆ t
ƒt
ks^t‚tt ˆ tƒƒt ˆ ttƒƒks€t‚tdƒ} t ˆ tƒ t¡ tˆ ƒtd|  dt d|  ˆ    t| ƒtd|  ˆ  ƒ  | dtˆ d ƒfƒ ¡sðt‚t ˆ tƒ d¡ tˆ ƒtd|  dt d|  ˆ    t| ƒtd|  ˆ  ƒ  | dtˆ d ƒfƒ ¡sXt‚tt ˆ tƒtƒdˆ  t ˆ d tƒ ks„t‚tt ˆ tƒˆ ƒtt ˆ tƒˆ ƒksªt‚tt‡ fdd„ƒ t ˆ tƒ t¡tdƒˆ  tˆ ttdƒ ƒ ksðt‚d S )Nr   r,   r-   rH   r/   rI   re   rV   é0   rS   é@   ià  rc   rd   r)   r.   r3   rJ   r:   c                      s   t ˆ tƒ d¡S r]   )r   r(   r<   r5   r\   r5   r6   r7   Y  r8   ztest_hermite.<locals>.<lambda>)r   r(   r>   r   r%   r   r   r   r	   r?   r   r   r
   rC   r   rA   r   r   r   r   r'   r&   r   ©rF   r5   r\   r6   Útest_hermite=  sX    "*6$2"ÿÿÿ 
ÿÿÿÿÿ 
ÿÿ,&ÿrw   c               
      sÔ  t dtƒdkst‚t dtƒtks$t‚t dtƒtd d ks>t‚t dtƒtd dt  ks\t‚t dtƒtd dtd   d ks‚t‚t dtƒtd dtd   dtd   d ks´t‚td	ƒ‰ tt ˆ tƒsÌt‚t ˆ t ƒd
ˆ  t ˆ tƒ ksît‚tt ˆ  tƒst‚t ˆ dƒttƒttj	ˆ d  ƒ ks,t‚t ˆ t
ƒt
ks@t‚tt ˆ tƒƒt ˆ ttƒƒksbt‚tdƒ} t ˆ tƒ t¡ tˆ ƒttj	 |  tˆ d|     t| ƒtˆ d|   ƒ  | dtˆ d ƒfƒ ¡sÒt‚t ˆ tƒ d¡ tˆ ƒttj	 |  tˆ d|     t| ƒtˆ d|   ƒ  | dtˆ d ƒfƒ ¡s:t‚tt ˆ tƒtƒˆ t ˆ d tƒ ksbt‚tt ˆ tƒˆ ƒtt ˆ tƒˆ ƒksˆt‚tt‡ fdd„ƒ t ˆ tƒ t¡tdƒˆ   tˆ ttdƒ ƒ ksÐt‚d S )Nr   r,   r-   r/   rH   rS   rR   é-   r)   r.   r3   r:   c                      s   t ˆ tƒ d¡S r]   )r   r(   r<   r5   r\   r5   r6   r7   {  r8   z#test_hermite_prob.<locals>.<lambda>)r   r(   r>   r   r%   r   r   r   r	   r?   r   r   r
   rC   r   rA   r   r   r   r   r'   r&   r   rv   r5   r\   r6   Útest_hermite_prob_  s<    &2"*"4ÿÿ4ÿÿ(&ÿry   c               	      sL  t dƒ‰ t ddd} tdtƒdks&t‚tdtƒt d ks>t‚tdtƒtd d dt  d ksdt‚tdtƒtd  d	 dtd  d  dt  d ksœt‚td
tƒtd ttƒ ksºt‚tˆ tƒ}t|tƒsÒt‚tˆ dƒdksät‚tˆ tƒdˆ  t ksþt‚tˆ t ƒtkst‚ttˆ tƒƒtˆ ttƒƒks6t‚tdƒ}tˆ tƒ 	t
¡ t
t| tˆ  |ƒ t|ƒd  |dˆ fƒ¡s‚t‚tˆ tƒ 	d¡ t
t| tˆ  |ƒ t|ƒd  |dˆ fƒ¡sÆt‚t| tƒ 	t
¡ ttƒt
t | t| d |ƒ t|ƒd  |d|  d fƒ ¡st‚t| tƒ 	d¡ ttƒt
t | t| d |ƒ t|ƒd  |d|  d fƒ ¡srt‚ttˆ tƒtƒtˆ d dtƒ ksšt‚t dƒ}tˆ  tƒttƒtˆ d t ƒ ksÌt‚tdtƒttƒtdt ƒ ksðt‚ttˆ  | tƒst‚ttdd„ ƒ ttdd„ ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nr)   r0   T)Únegativer   r,   r-   r/   rS   rJ   r.   r3   r:   ra   c                   S   s
   t dtƒS r4   )r!   r(   r5   r5   r5   r6   r7   ©  r8   ztest_laguerre.<locals>.<lambda>c                   S   s   t tddƒtƒS )Nr;   r-   )r!   r   r(   r5   r5   r5   r6   r7   ª  r8   c                      s   t ˆ tƒ d¡S rZ   ©r!   r(   r<   r5   r\   r5   r6   r7   «  r8   c                      s   t ˆ tƒ d¡S r]   r{   r5   r\   r5   r6   r7   ¬  r8   )r   r!   r(   r>   r   r@   r   r   r
   rC   r   rA   r   r   r   r   r%   r'   rB   r&   )r0   rE   rF   r3   r5   r\   r6   Útest_laguerre  sN    &8
"*ÿ
*ÿ
*ÿÿ
*ÿÿ
(*$r|   c               	      sx  t dƒ‰t dƒ} t dƒ‰ tdˆ tƒdks,t‚tdˆ tƒt ˆ  d ksJt‚tdˆ tƒ ¡ td d ˆ d t  ˆ d ˆ d  d   ¡ ksŽt‚tdˆ tƒ ¡ td  d ˆ d td  d  ˆ d ˆ d  t d  ˆ d ˆ d  ˆ d  d   ¡ ksüt‚td	ƒD ]&}t|dtƒ ¡ t|tƒkst‚qtˆ| tƒ}t|tƒsHt‚tˆdtƒtˆtƒksdt‚tˆˆ dƒt	ˆ ˆ ˆ ƒks„t‚t d
dd}t|ˆ t
ƒd| t
 ks®t‚t|ˆ t
 ƒt
ksÆt‚ttˆˆ tƒtƒtˆd ˆ d tƒ ksôt‚tdƒ}ttˆˆ tƒˆ ƒ tt|ˆ tƒˆ  ˆ  |dˆd fƒ¡s<t‚ttˆˆ tƒƒtˆtˆ ƒttƒƒksft‚tˆˆ tƒ t¡ tˆ ˆ d ƒtt| tˆ |ƒ t|ƒt|ˆ  d ƒ  |dˆfƒ tˆƒ ¡sÐt‚tˆˆ tƒ d¡ tˆ ˆ d ƒtt| tˆ |ƒ t|ƒt|ˆ  d ƒ  |dˆfƒ tˆƒ ¡s:t‚tt‡ fdd„ƒ tt‡ ‡fdd„ƒ tt‡ ‡fdd„ƒ d S )Nr)   r0   Úalphar   r,   r-   r/   rS   rW   ÚpTr1   r.   r3   r:   c                      s   t dˆ tƒS r4   )r   r(   r5   )r}   r5   r6   r7   Ù  r8   z%test_assoc_laguerre.<locals>.<lambda>c                      s   t ˆˆ tƒ d¡S rZ   ©r   r(   r<   r5   ©r}   r)   r5   r6   r7   Ú  r8   c                      s   t ˆˆ tƒ d¡S rK   r   r5   r€   r5   r6   r7   Û  r8   )r   r   r(   r>   r^   rq   r#   r@   r!   r   r   r   r
   rA   r   r   rC   r   r   r   r'   rB   r&   )r0   ÚirE   r~   rF   r5   r€   r6   Útest_assoc_laguerre¯  sj    .ÿ8ÿÿ$ ÿ
$ÿ
ÿ
"ÿÿÿÿ
"ÿÿÿÿ
r‚   N)BZsympy.concrete.summationsr   Zsympy.core.functionr   r   Zsympy.core.numbersr   r   r   r   Zsympy.core.singletonr	   Zsympy.core.symbolr
   r   Z(sympy.functions.combinatorial.factorialsr   r   r   Z$sympy.functions.elementary.complexesr   Z&sympy.functions.elementary.exponentialr   Z#sympy.functions.elementary.integersr   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   Z'sympy.functions.special.gamma_functionsr   Zsympy.functions.special.hyperr   Z#sympy.functions.special.polynomialsr   r   r   r   r   r   r   r   r   r   r    r!   r"   Zsympy.polys.orthopolysr#   Zsympy.polys.polyrootsr$   Zsympy.core.exprr%   r&   Zsympy.testing.pytestr'   r(   rG   rM   r`   rl   rs   rw   ry   r|   r‚   r5   r5   r5   r6   Ú<module>   s8   <@475C"".