A new elementary algorithm for proving q-hypergeometric identities

摘要

We give a fast elementary algorithm to get a small number n_1 for an admissible q-proper-hypergeometric identity ∑_k F(n, k) = G(n), n≥n_0 such that we can prove the identity by checking its correctness for n (n_0 ≤ n ≤ 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.