Integrals of products of four modified Bessel functions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909994367057920 |
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| author | Gaunt, Robert E. |
| author_facet | Gaunt, Robert E. |
| contents | We evaluate definite integrals involving the product of four modified Bessel functions of the first and second kind and a power function. We provide general formulas expressed in terms of the Meijer $G$-function and generalized hypergeometric and Lauricella $F_C$ functions, and study a number of special cases in which the integrals can be evaluated in terms of simpler special functions or indeed take an elementary form. As a consequence, we deduce some new formulas for definite integrals of products of four Airy functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12590 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrals of products of four modified Bessel functions Gaunt, Robert E. Classical Analysis and ODEs Primary 33C10, 33C20, 33C60 We evaluate definite integrals involving the product of four modified Bessel functions of the first and second kind and a power function. We provide general formulas expressed in terms of the Meijer $G$-function and generalized hypergeometric and Lauricella $F_C$ functions, and study a number of special cases in which the integrals can be evaluated in terms of simpler special functions or indeed take an elementary form. As a consequence, we deduce some new formulas for definite integrals of products of four Airy functions. |
| title | Integrals of products of four modified Bessel functions |
| topic | Classical Analysis and ODEs Primary 33C10, 33C20, 33C60 |
| url | https://arxiv.org/abs/2601.12590 |