Approximating the coefficients of the Bessel functions

2025/10/11 by Andrew Yao, Andrew Chi-Chih Yao, Yao, Andrew · 1 citation
Mathematics · #Analytic and geometric function theory #Bessel function #Bilinear interpolation #Differential Equations and Boundary Problems #Exponential function #Holomorphic function #Mathematical functions and polynomials #Root (linguistics) #Type (biology)

paper · pdf · doi:10.48550/arxiv.2510.10370

openalex publication_date 2025/10/11 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

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| →∞ regime for the type A and D root systems and over the |θ₀ N|→ ∞, (θ₁)/(θ₀ N)→ c∈ℂ regime for the type BC root system. We also establish equivalent conditions over the θN → c∈ℂ regime for the type A and D root systems and over the θ₀ N→ c₀∈ℂ, (θ₁)/(θ₀ N)→ c₁∈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.

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