SumTools[IndefiniteSum]
AccurateSummation
compute closed forms of indefinite sums using accurate summation
Calling Sequence
Parameters
Description
Examples
References
AccurateSummation(T, n)
T
-
function of n
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 Tn=Gn+1−Gn if the algorithm succeeds in constructing one. Otherwise, it returns FAIL.
withSumToolsIndefiniteSum:
T≔Γn+1−Γn−Ψn
AccurateSummationT,n
n4−n3−6n2−6n−5Γn+1−Γn−Ψnn2+n+3−n5−n4−10n3−9n2−2Γn+2−Γn+1−Ψn+1nn2+n+3+n+1n3−5n2+4n−2Γn+3−Γn+2−Ψn+2nn2+n+3
Note that since T is not a hypergeometric term of n, Gosper's algorithm fails to compute an anti-difference:
HypergeometricT,n
FAIL
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.
See Also
SumTools[IndefiniteSum][Indefinite]
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