Constructive extensions of three summation formulas for q-series and their applications to Bailey pairs

摘要

This paper is devoted to three constructive extensions associated with the Pfaff-Saalschutz (3)phi(2), Watson's (6)phi(5), and Jackson's (8)phi(7) summation formulas in basic hypergeometric series. All these lead to new general recurrence approaches to well-known Bailey pairs and well-poised Bailey pairs, as well as the emergence of new Pfaff-Saalschutz pairs. Some new applications to q-series are also investigated.