$q$-Rational Reduction and $q$-Analogues of Series for $\pi$
Combinatorics
2022-08-02 v2 Number Theory
Abstract
In this paper, we present a -analogue of the polynomial reduction which was originally developed for hypergeometric terms. Using the -Gosper representation, we describe the structure of rational functions that are summable when multiplied with a given -hypergeometric term. The structure theorem enables us to generalize the -polynomial reduction to the rational case, which can be used in the automatic proof and discovery of -identities. As applications, several -analogues of series for are presented.
Keywords
Cite
@article{arxiv.2203.16047,
title = {$q$-Rational Reduction and $q$-Analogues of Series for $\pi$},
author = {Rong-Hua Wang and Michael X. X. Zhong},
journal= {arXiv preprint arXiv:2203.16047},
year = {2022}
}