§ E¯d¸ãó—dd„Zd„ZdS)écóŽ—| ¦«}| |||z¦«}| ¦«}||z S)ay Takes as input a polynomial expression and the variable used to construct it and returns the difference between function's value when the input is incremented to 1 and the original function value. If you want an increment other than one supply it as a third argument. Examples ======== >>> from sympy.abc import x, y, z >>> from sympy.series.kauers import finite_diff >>> finite_diff(x**2, x) 2*x + 1 >>> finite_diff(y**3 + 2*y**2 + 3*y + 4, y) 3*y**2 + 7*y + 6 >>> finite_diff(x**2 + 3*x + 8, x, 2) 4*x + 10 >>> finite_diff(z**3 + 8*z, z, 3) 9*z**2 + 27*z + 51 )ÚexpandÚsubs)Ú expressionÚvariableÚ incrementÚ expression2s ú3lib/python3.11/site-packages/sympy/series/kauers.pyÚ finite_diffr sI€ð*×"Ò"Ñ$Ô$€JØ—/’/ (¨H°yÑ,@ÑAÔA€KØ×$Ò$Ñ&Ô&€KØ ˜Ñ #Ð#ócór—|j}|jD]'}| |d|ddz¦«}Œ(|S)a© Takes as input a Sum instance and returns the difference between the sum with the upper index incremented by 1 and the original sum. For example, if S(n) is a sum, then finite_diff_kauers will return S(n + 1) - S(n). Examples ======== >>> from sympy.series.kauers import finite_diff_kauers >>> from sympy import Sum >>> from sympy.abc import x, y, m, n, k >>> finite_diff_kauers(Sum(k, (k, 1, n))) n + 1 >>> finite_diff_kauers(Sum(1/k, (k, 1, n))) 1/(n + 1) >>> finite_diff_kauers(Sum((x*y**2), (x, 1, n), (y, 1, m))) (m + 1)**2*(n + 1) >>> finite_diff_kauers(Sum((x*y), (x, 1, m), (y, 1, n))) (m + 1)*(n + 1) ééÿÿÿÿr)ÚfunctionÚlimitsr)ÚsumrÚls r Úfinite_diff_kauersrsB€ð*Œ|€HØ ŒZð3ð3ˆØ—=’=  1¤ q¨¤v°¡zÑ2Ô2ˆˆØ €Or N)r)r r©r r úrs2ðð$ð$ð$ð$ð4ððððr