English

Erd\'{e}lyi-type integrals for $F_K$ function and their $q$-analogues

General Mathematics 2026-02-24 v2

Abstract

In this paper, we revisit the recent result of Luo, Xu, and Raina [Fractal Fract. 6 (3) (2022)] on an Erd\'{e}lyi-type integral for Saran's three-variable hypergeometric function FKF_K. We provide a new proof of this integral and derive an attractive new integral related to Appell's function F2F_2. A further extension on the LL-variable FKF_K function, which appears in physics, is also discussed. Furthermore, we prove various qq-Erd\'{e}lyi-type integrals for the qq-analogue of the FKF_K-function. An interesting discrete analogue is also included. We also provide a valuable compilation of the sources for known Erd\'{e}lyi-type integrals of many different hypergeometric functions in the Appendix.

Keywords

Cite

@article{arxiv.2512.11937,
  title  = {Erd\'{e}lyi-type integrals for $F_K$ function and their $q$-analogues},
  author = {Liang-Jia Guo and Min-Jie Luo},
  journal= {arXiv preprint arXiv:2512.11937},
  year   = {2026}
}
R2 v1 2026-07-01T08:22:49.745Z