Q-Rational reduction and q-analogues of series for π. (May 2023) - Wang, Rong-Hua; Zhong, Michael X.X.
Abstract: In this paper, we present a q -analogue of the polynomial reduction which was originally developed for hypergeometric terms. Using the q -Gosper representation, we describe the structure of rational functions that are summable when multiplied with a given q -hypergeometric term. The structure theorem enables us to generalize the q -polynomial reduction to the rational case, which can be used in the automatic proof and discovery of q -identities. As applications, several q -analogues of series for π are presented.