
    hN                     p    S SK Jr  S SK Jr  S SKJrJrJrJrJrJ	r	  S SK
Jr  S SKJrJr  S SKJr  S rS rg	)
    )finite_diff)finite_diff_kauers)xyzmnw)pi)cossin)Sumc                     [        [        S-  S[        -  -   S-   [        5      S[        -  S-   :X  d   e[        [        S-  S[        S-  -  -   S[        -  -   S-   [        5      S[        S-  -  S[        -  -   S-   :X  d   e[        [        S-  S[        -  -
  S-   [        5      S[        -  S-
  :X  d   e[        [        S-  S[        -  -   S-
  [        5      S[        -  S-   :X  d   e[        [        [        5      [        [        S-  5      [        [        5      * [        [        [        S-  -   5      -   :X  d   e[        [        [        5      [        [        S-  5      [        [        5      * [        [        [        S-  -   5      -   :X  d   e[        [        S-  S[        -  -
  S-   [        S5      S[        -  :X  d   e[        [        S-  S[        -  -
  S-   [        S5      S[        -  S-   :X  d   eg )N                     )	r   r   r   r   r
   r   r   r   r	        V/var/www/html/shao/venv/lib/python3.13/site-packages/sympy/series/tests/test_kauers.pytest_finite_diffr   	   s   q!taczA~q)QqS1W444q!ta1f}qs*Q.2a1fqslQ6FFFFq!taczA~q)QqS1W444q!taczA~q)QqS1W444s1vq"Q$'CF7SRT]+BBBBs1vq"Q$'CF7SRT]+BBBBq!taczA~q!,!333q!taczA~q!,!a777r   c            	         [        [        [        S-  [        S[        45      5      [        S-   S-  :X  d   e[        [        [        [        S[
        45      5      [
        S-   :X  d   e[        [        [        [        -  [        S[
        4[        S[        45      5      [
        S-   [        S-   -  :X  d   e[        [        [        [        S-  -  [        S[
        4[        S[        45      5      [        S-   S-  [
        S-   -  :X  d   eg )Nr   r   )r   r   r   r	   r   r   r   r   r   test_finite_diff_kauersr      s    c!Q$Aq	23AzAAAc!aAY/0QU;;;c1Q3!QQ1I>?AEAPQE?RRRc1QT6Q1I1ayABq1uqjRSVWRWFXXXXr   N)sympy.series.kauersr   r   	sympy.abcr   r   r   r   r	   r
   sympy.core.numbersr   (sympy.functions.elementary.trigonometricr   r   sympy.concrete.summationsr   r   r   r   r   r   <module>r"      s%    + 2 & & ! ? )8Yr   