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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1978 Jan;75(1):40–42. doi: 10.1073/pnas.75.1.40

Decision procedure for indefinite hypergeometric summation

R William Gosper Jr 1
PMCID: PMC411178  PMID: 16592483

Abstract

Given a summand an, we seek the “indefinite sum” S(n) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited which, given an, finds those S(n) with the property [Formula: see text] With this algorithm, we can determine, for example, the three identities [Formula: see text] [Formula: see text] and [Formula: see text] and we can also conclude that [Formula: see text] is inexpressible as S(m) - S(0), for any S(n) satisfying Eq. 2.

Keywords: algorithm, binomial coefficient identities, closed form, symbolic computation, linear recurrences

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