Basic hypergeometric identities derived from three-term relations
Classical Analysis and ODEs
2025-11-12 v2
Abstract
In 2015, Ebisu presented a new method for finding hypergeometric identities based on three-term relations for the hypergeometric series. By using this method, he derived almost all of the previously known hypergeometric identities, as well as many new ones. In this paper, we derive several basic hypergeometric identities, including both well-known and not widely known ones, by applying a -analogue of Ebisu's method to three-term relations for the basic hypergeometric series.
Keywords
Cite
@article{arxiv.2508.05965,
title = {Basic hypergeometric identities derived from three-term relations},
author = {Yuka Yamaguchi},
journal= {arXiv preprint arXiv:2508.05965},
year = {2025}
}
Comments
13 pages, This version integrates the results from a previously submitted paper (arXiv:2505.20798) into this manuscript