The generalized q-operator r?s and its applications in q-identities

Abstract

Based on the basic hypergeometric series r?s, we construct a new generalized q-operator r?s (a1, . . . , ar b1, . . . , bs ; q, ?c?) and obtain some of its identities. Using these identities, we generalize several well-known q-identities, such as the q-Gauss sum, the q-Chu-Vandermonde sum, and the q-Pffaf-Saalschütz sum.