A 2-LINE ALGORITHM FOR PROVING TERMINATING HYPERGEOMETRIC IDENTITIES

We give an algorithm that takes a proposed terminating hypergeometric identity of the form Sigma/k F(n,k) = f(n), n greater than or equal to n(0) and directly from n(0), F(n, k), and f(n) computes an explicit i nteger n(1) such that if the equality holds for all n is an element of {n(0), n(0) + 1,..., n(1)} then Sigma(k) F(n, k) = f(n) for all n gre ater than or equal to n(0); otherwise the proposed identity is obvious ly false. This paper contains the first estimate for n(1). (C) 1996 Ac ademic Press, Inc.