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 . We provide a new proof of this integral and derive an attractive new integral related to Appell's function . A further extension on the -variable function, which appears in physics, is also discussed. Furthermore, we prove various -Erd\'{e}lyi-type integrals for the -analogue of the -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}
}