Decision procedure for indefinite hypergeometric summation

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.