
    khN                     p    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	 d dl
mZ d dlmZmZ d dlmZ d Zd Zy	)
    )finite_diff)finite_diff_kauers)xyzmnw)pi)cossin)Sumc                     t        t        dz  dt        z  z   dz   t              dt        z  dz   k(  sJ t        t        dz  dt        dz  z  z   dt        z  z   dz   t              dt        dz  z  dt        z  z   dz   k(  sJ t        t        dz  dt        z  z
  dz   t              dt        z  dz
  k(  sJ t        t        dz  dt        z  z   dz
  t              dt        z  dz   k(  sJ t        t        t              t        t        dz        t        t               t        t        t        dz  z         z   k(  sJ t        t        t              t        t        dz        t        t               t        t        t        dz  z         z   k(  sJ t        t        dz  dt        z  z
  dz   t        d      dt        z  k(  sJ t        t        dz  dt        z  z
  dz   t        d      dt        z  dz   k(  sJ y )N                     )	r   r   r   r   r
   r   r   r   r	        Z/var/www/teggl/fontify/venv/lib/python3.12/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            	         t        t        t        dz  t        dt        f            t        dz   dz  k(  sJ t        t        t        t        dt
        f            t
        dz   k(  sJ t        t        t        t        z  t        dt
        ft        dt        f            t
        dz   t        dz   z  k(  sJ t        t        t        t        dz  z  t        dt
        ft        dt        f            t        dz   dz  t
        dz   z  k(  sJ y )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   