A new elementary algorithm for proving q-hypergeometric identities

We give a fast elementary algorithm to get a small number n(1) for an admissible q-proper-hypergeometric identity [GRAPHICS] such that we can prove the identity by checking its correctness for n (n(0) less than or equal to n less than or equal to n(1)). For example, we get n(1) = 191 for the q-Vandermonde-Chu identity, n(1) = 70 for a finite version of Jacobi's triple product identity and n(1) = 209 for an identity due to L.J. Rogers. (C) 2003 Published by Elsevier Science Ltd.