Erdélyi-type integrals for $F_K$ function and their $q$-analogues
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908845488472064 |
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| author | Guo, Liang-Jia Luo, Min-Jie |
| author_facet | Guo, Liang-Jia Luo, Min-Jie |
| contents | 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 $F_2$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Erdélyi-type integrals for $F_K$ function and their $q$-analogues Guo, Liang-Jia Luo, Min-Jie General Mathematics 33C05, 33C65, 33C70, 33D15, 33D70 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 $F_2$. 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. |
| title | Erdélyi-type integrals for $F_K$ function and their $q$-analogues |
| topic | General Mathematics 33C05, 33C65, 33C70, 33D15, 33D70 |
| url | https://arxiv.org/abs/2512.11937 |