SumTools[IndefiniteSum]
Polynomial
compute closed forms of indefinite sums of polynomials
Calling Sequence
Parameters
Description
Examples
Polynomial(f, k)
f
-
polynomial in k
k
name
The Polynomial(f, k) command computes a closed form of the indefinite sum of f with respect to k.
Polynomials are summed using a formula based on Bernoulli polynomials.
withSumToolsIndefiniteSum:
p≔68y2−17x2y2−98xy3−36x4y+40x3y2+22x2y3
p≔−36x4y+40x3y2+22x2y3−17x2y2−98xy3+68y2
dpx≔Polynomialp,x
dpx≔3916y2x−60x2y3+1583xy3+223x3y3−773x3y2+372x2y2+10y2x4−365yx5+18x4y−12yx3+65yx
expandp−evaldpx,x=x+1−dpx
0
dpy≔Polynomialp,y
dpy≔−18y2x4+18x4y+403x3y3−503x2y3+683y3−20x3y2+14x2y2−34y2+203yx3−176x2y+343y+112x2y4−492xy4+49xy3−492y2x
expandp−evaldpy,y=y+1−dpy
See Also
SumTools[IndefiniteSum][Indefinite]
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