The Askey–Wilson Integral and Extensions

Abstract

By means of the q-derivative operator method, we review the q-beta integrals of Askey–Wilson and Nassrallah–Rahman. More integrals are evaluated by the author, making use of Bailey’s identity of well-poised bilateral 6ψ6-series as well as the extended identity of Karlsson–Minton type for parameterized well-poised bilateral q-series.

Keywords

• basic hypergeometric series
• Bailey’s identity for well-poised 6<i>ψ</i>6-series
• the <i>q</i>-derivative operator
• Askey–Wilson integral
• Nassrallah–Rahman integral