
    (phF                     X    S r  SSKrS rS rS r\S:X  a  \" 5         gg! \ a     N f = f)z-Precompute series coefficients for log-Gamma.    Nc                     [         R                  " S5         [        SU S-   5       Vs/ s H+  n[         R                  " SU-  5      SU-  SU-  S-
  -  -  PM-     nnS S S 5        U$ s  snf ! , (       d  f       W$ = f)Nd         )mpmathworkdpsrange	bernoulli)Nncoeffss      U/var/www/html/venv/lib/python3.13/site-packages/scipy/special/_precompute/loggamma.pystirling_seriesr   	   s}    		 AE?,*a ""1Q3'1acAg7* 	 , 
 M, 
	 Ms   A,2A'A,'A,,
A;c                 4   / n[         R                  " S5         UR                  [         R                  * 5        [	        SU S-   5       H1  nUR                  SU-  [         R
                  " U5      -  U-  5        M3     S S S 5        U$ ! , (       d  f       U$ = f)Nr   r   r   )r   r   appendeulerr	   zeta)r   r   r   s      r   taylor_series_at_1r      sw    F		v||m$q!a%AMM2'&++a.023 ! 
 M	 
	 Ms   A%B
Bc            
      
   [        [        5        [        5         [        S5      S S S2    V s/ s H  n [        R                  " U SSSS9PM     nn [        S5      S S S2    V s/ s H  n [        R                  " U SSSS9PM     nn [        S5        [        S5        [        S	R                  U5      5        [        5         [        S
5        [        S5        [        S	R                  U5      5        [        5         g s  sn f s  sn f )N   r      r   )	min_fixed	max_fixed   zStirling series coefficientsz----------------------------
zTaylor series coefficientsz--------------------------)print__doc__r   r   nstrr   join)xstirling_coeffstaylor_coeffss      r   mainr$      s    	'N	G / 24R4 8: 81 {{1bAC 8  : 14TrT:<: [[B!qA:  <	
()	
()	$))O
$%	G	
&'	
&'	$))M
"#	G:<s   !C;#!D __main__)r   r   ImportErrorr   r   r$   __name__     r   <module>r*      sH    3	
" zF K  		s     ))