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In many cases one may encounter an integral which is of $q$-Mellin--Barnestype. These integrals are easily evaluated using theorems which have a longhistory dating back to Slater, Askey, Gasper, Rahman and others. We derive someinteresting $q$-Mellin--Barnes integrals and using them we derivetransformation and summation formulas for nonterminating basic hypergeometricfunctions. The cases which we treat include ratios of theta functions, theAskey--Wilson moments, nonterminating well-poised ${}_3\phi_2$, nonterminatingvery-well-poised ${}_5W_4$, ${}_8W_7$, products of two nonterminating${}_2\phi_1$'s, square of a nonterminating well-poised ${}_2\phi_1$, andnonterminating ${}_{12}W_{11}$ and ${}_{10}W_9$.

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