A two-line algorithm for proving q-hypergeometric identities

[摘要] We show that q-hypergeometric identities Sigma(k)F(n,k)=1 can be proved by checking that they are correct for only finitely many, N say, values of n. We give a specific a priori formula for N, as a polynomial of degree 24 in the parameters of F(n, k). We see this because of the presence of ''q'', the estimates of N can be made smaller than the general estimates that were found in the author's thesis (''Contributions to the Proof Theory of Hypergeometric Identities,'' pp. 1-83, Ph.D. thesis, University of Pennsylvania, Philadelphia, 1993). As an example of 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 correct, by direct computation. (C) 1997 Academic Press.

[发布日期] 1997-09-01