Approximating the coefficients of the Bessel functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912976991158272 |
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| author | Yao, Andrew |
| author_facet | Yao, Andrew |
| contents | We determine equivalent conditions between the asymptotic coefficients of the Bessel generating functions of a sequence of probability measures and the asymptotic expected values of power sums when their inputs are sampled from these measures. We establish these conditions over the $|θN| \rightarrow\infty$ regime for the type A and D root systems and over the $|θ_0 N|\rightarrow \infty, \frac{θ_1}{θ_0 N}\rightarrow c\in\mathbb{C}$ regime for the type BC root system. We also establish equivalent conditions over the $θN \rightarrow c\in\mathbb{C}$ regime for the type A and D root systems and over the $θ_0 N\rightarrow c_0\in\mathbb{C}, \frac{θ_1}{θ_0 N}\rightarrow c_1\in\mathbb{C}$ regime for the type BC root system that generalize existing results. Furthermore, we determine the asymptotics of the coefficients of the Bessel functions over the regimes that we have mentioned. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximating the coefficients of the Bessel functions Yao, Andrew Classical Analysis and ODEs Mathematical Physics Combinatorics Operator Algebras Probability We determine equivalent conditions between the asymptotic coefficients of the Bessel generating functions of a sequence of probability measures and the asymptotic expected values of power sums when their inputs are sampled from these measures. We establish these conditions over the $|θN| \rightarrow\infty$ regime for the type A and D root systems and over the $|θ_0 N|\rightarrow \infty, \frac{θ_1}{θ_0 N}\rightarrow c\in\mathbb{C}$ regime for the type BC root system. We also establish equivalent conditions over the $θN \rightarrow c\in\mathbb{C}$ regime for the type A and D root systems and over the $θ_0 N\rightarrow c_0\in\mathbb{C}, \frac{θ_1}{θ_0 N}\rightarrow c_1\in\mathbb{C}$ regime for the type BC root system that generalize existing results. Furthermore, we determine the asymptotics of the coefficients of the Bessel functions over the regimes that we have mentioned. |
| title | Approximating the coefficients of the Bessel functions |
| topic | Classical Analysis and ODEs Mathematical Physics Combinatorics Operator Algebras Probability |
| url | https://arxiv.org/abs/2510.10370 |