English

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 2F1{}_{2} F_{1} 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 qq-analogue of Ebisu's method to three-term relations for the 2ϕ1{}_{2} \phi_{1} 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