Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO
No
Adv. Appl. Math.
Article
Científica
1
0.733
01/06/2023
000952717000001
2-s2.0-85150058242
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 interesting q-Mellin–Barnes integrals and using them we derive transformation and summation formulas for nonterminating basic hypergeometric functions. The cases which we treat include ratios of theta functions, the Askey–Wilson moments, nonterminating well-poised ?23, nonterminating very-well-poised W45, W78, products of two nonterminating ?12's, square of a nonterminating well-poised ?12, a nonterminating W910, two nonterminating W1112's and several nonterminating summations which arise from the Askey–Roy and Gasper integrals. © 2023
Askey-Wilson polynomials; Askey–wilson moment; Basic hypergeometric functions; Integral representation; Mellin-Barnes integrals; Nonterminating basic hypergeometric function; Nonterminating summation; Nonterminating transformation; Q calculus; Q-mellin–barnes integral