A 2-LINE ALGORITHM FOR PROVING Q-HYPERGEOMETRIC IDENTITIES

We show that q-hypergeometric identities Sigma(k)F(n,k)=1 can be prove d by checking that they are correct for only finitely many, N say, val ues of n. We give a specific a priori formula for N, as a polynomial o f degree 24 in the parameters of F(n, k). We see this because of the p resence of ''q'', the estimates of N can be made smaller than the gene ral estimates that were found in the author's thesis (''Contributions to the Proof Theory of Hypergeometric Identities,'' pp. 1-83, Ph.D. th esis, University of Pennsylvania, Philadelphia, 1993). As an example o f the method we show that the q-Vandermonde identity can be proved by ''only'' checking that its first 2358 cases (i.e., values of n) are co rrect, by direct computation. (C) 1997 Academic Press.