Q-Gosper algorithm and simple Bailey pairs. (November 2022) - Bian, Ke-Xin; Liu, Yue; Mu, Yan-Ping
Abstract: We present a method of constructing simple Bailey pairs based on the q -Gosper algorithm. We illustrate the method by determining Gosper-summable q -hypergeometric terms of the form ( a ; q ) k ( q ; q ) k z k . We further give some simple Bailey pairs in more complicated forms. As applications, we derive some summation and transformation formulas for q -series.