
    gN                     r    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d	S )
    )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 d S )N                     )	r   r   r   r   r
   r   r   r   r	        Z/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/series/tests/test_kauers.pytest_finite_diffr   	   s   q!taczA~q))QqS1W4444q!ta1f}qs*Q.22a1fqslQ6FFFFFq!taczA~q))QqS1W4444q!taczA~q))QqS1W4444s1vvq"Q$''CFF7SRT]]+BBBBBs1vvq"Q$''CFF7SRT]]+BBBBBq!taczA~q!,,!3333q!taczA~q!,,!a777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 d S )Nr   r   )r   r   r   r	   r   r   r   r   r   test_finite_diff_kauersr      s    c!Q$Aq	2233AzAAAAc!aAY//00QU;;;;c1Q3!QQ1I>>??AEAPQE?RRRRc1QT6Q1I1ayAABBq1uqjRSVWRWFXXXX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 2 2 2 2 2 & & & & & & & & & & & & & & & & ! ! ! ! ! ! ? ? ? ? ? ? ? ? ) ) ) ) ) )8 8 8Y Y Y Y Yr   