Nonterminating transformations and summations associated with some q-Mellin-Barnes integrals

In many cases one may encounter an integral which is of q-Mellin-Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some interest-ing q-Mellin-Barnes integrals and using them we derive trans-formation and summation formulas for nonterminating basic hypergeometric functions. The cases which we treat include ratios of theta functions, the Askey-Wilson moments, non-terminating well-poised 342, nonterminating very-well-poised 5W4, 8W7, products of two nonterminating 241's, square of a nonterminating well-poised 241, a nonterminating 10W9, two nonterminating 12W11's and several nonterminating summa-tions which arise from the Askey-Roy and Gasper integrals. Published by Elsevier Inc.