A Two-Line Algorithm for Proving Terminating Hypergeometric Identities*

We give an algorithm that takes a proposed terminating hypergeometric identity of the form F n,k.sf n., nGn0 k and directly from n0, F n, k., and f n.computes an explicit integer n1such that if the equality holds for all ng n0, n0q1, . . . , n14then kF n, k.sf n. for all nGn0; otherwise the proposed identity is obviously false. This paper contains the first estimate for n1.