SumTools[IndefiniteSum][AccurateSummation] - compute closed forms of indefinite sums using accurate summation
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Calling Sequence
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AccurateSummation(T, n)
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Parameters
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T
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function of n
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n
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name; specifies summation index
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Description
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The AccurateSummation(T, n) command solves the problem of indefinite summation using accurate summation.
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The output from AccurateSummation is a function such that if the algorithm succeeds in constructing one. Otherwise, it returns FAIL.
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Examples
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Note that since T is not a hypergeometric term of n, Gosper's algorithm fails to compute an anti-difference:
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References
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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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