General $q$-series transformations based on Abel's lemma on summation by parts and their applications
Classical Analysis and ODEs
2023-09-25 v3
Abstract
In this paper, we establish three new and general transformations with sixteen parameters and bases via Abel's lemma on summation by parts. As applications, we set up a lot of new transformations of basic hypergeometric series. Among include some new results of Gasper and Rahman's quadratic, cubic, and quartic transformations. Furthermore, we put forward the so-called -type transformation with arbitrary degree to unify such multibasic transformations. Some special -type transformations are presented.
Keywords
Cite
@article{arxiv.2307.07968,
title = {General $q$-series transformations based on Abel's lemma on summation by parts and their applications},
author = {Jianan Xu and Xinrong Ma},
journal= {arXiv preprint arXiv:2307.07968},
year = {2023}
}