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  z  gk    sJ d	 t          d          D             }t          t          |                    dd
dz
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dz  z   dz
  z  gk    sJ d t          d          D             }t          t          |                    dddz
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  z  ddz  z  dz  z   dz
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  dz   z  gk    sJ fdt          d          D             }t          || d          }t	          |          dk    sJ t	          |          d| dz   z  dz
  z  k    sJ d S )Nzx,tc                 ,    g | ]}t          |          S  r   .0ks     `/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/series/tests/test_approximants.py
<listcomp>z%test_approximants.<locals>.<listcomp>	   s    %%%aq%%%                   c                 R    g | ]$}t          |          t          |d z             z   %S r   )r   r   r   s     r   r   z%test_approximants.<locals>.<listcomp>   s-    444Qq)AaC..	 444r   c                 2    g | ]}t          |          d z  S r   r   r   s     r   r   z%test_approximants.<locals>.<listcomp>   s"    (((q1(((r      i#   	   %               2   ?   4      c           	      j    g | ].t          fd t          dz             D                       /S )c              3   D   K   | ]}t          |          |z  z  V  d S )Nr   )r   ir   xs     r   	<genexpr>z/test_approximants.<locals>.<listcomp>.<genexpr>   s4      44AXa]]1a4444444r   r   )sumrange)r   r   r,   s    @r   r   z%test_approximants.<locals>.<listcomp>   sD    HHH44444qs444	4	4HHHr   T)simplify)r   r/   listr   next)tgpyr,   s       @r   test_approximantsr8      sz   5>>DAq%%599%%%AQ  	
BAJ1q1Q37+a!eadQhl-CDG G G G44%))444AQ  	
BAJ1q1Q37+RAA->?B B B B((eBii(((AQ  	
CQK"Q$(QqS1W-1r	Bq!tGbdNQ<N/O	AqD2a4"	r!Q$wA~23
Q$1q1a4!AqD&=1Q3.23	57 7 7 7 	IHHHeBiiHHHAQD)))A77a<<<<77b!QU)a-(((((((r   N)
sympy.seriesr   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr   %sympy.functions.combinatorial.numbersr   r   r8   r   r   r   <module>r=      sl    % % % % % % % % % % % % = = = = = = D D D D D D D D) ) ) ) )r   