Erdélyi-type integrals for F_K function and their q-analogues

2025/12/12 by L. Guo, Guo, Liang-Jia, Min-Jie Luo +1
Mathematics · Physics and Astronomy · #33C05 #33C65 #33C70 #33D15 #33D70 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2512.11937

openalex publication_date 2025/12/12 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

In this paper, we revisit the recent result of Luo, Xu, and Raina [Fractal Fract. 6 (3) (2022)] on an Erdélyi-type integral for Saran's three-variable hypergeometric function F_K. We provide a new proof of this integral and derive an attractive new integral related to Appell's function F₂. A further extension on the L-variable F_K function, which appears in physics, is also discussed. Furthermore, we prove various q-Erdélyi-type integrals for the q-analogue of the F_K-function. An interesting discrete analogue is also included. We also provide a valuable compilation of the sources for known Erdélyi-type integrals of many different hypergeometric functions in the Appendix.

Citations

• Asymptotics of Saran's hypergeometric function F_K
• Euler--Mellin integrals and A-hypergeometric functions

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