compute closed forms of indefinite sums using accurate summation
function of n
name; specifies summation index
The AccurateSummation(T, n) command solves the problem of indefinite summation using accurate summation.
The output from AccurateSummation is a function G such that T⁡n=G⁡n+1−G⁡n if the algorithm succeeds in constructing one. Otherwise, it returns FAIL.
T ≔ GAMMA⁡n+1−GAMMA⁡n−Ψ⁡n
Note that since T is not a hypergeometric term of n, Gosper's algorithm fails to compute an anti-difference:
Abramov, S.A. and van Hoeij, M. "Integration of Solutions of Linear Functional Equations." Integral Transformations and Special Functions, (1999): 3-12. Vol. 8. No. 1-2.
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