a  ¬>> 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)Z expressionÚvariableÚ incrementZ expression2©rúc/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/series/kauers.pyÚ finite_diffsrcCs.|j}|jD]}| |d|ddˇ}q |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) éé˙˙˙˙r)ÚfunctionZlimitsr)Úsumr ÚlrrrÚfinite_diff_kauerss rN)r)rrrrrrÚs