Uniform asymptotic expansions for the zeros of Bessel functions

2023/10/24 by T. M. Dunster, Dunster, T. M. · 4 citations
Mathematics · #33C10 #34E05 #34E20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2310.16016

openalex publication_date 2023/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Reformulated uniform asymptotic expansions are derived for ordinary differential equations having a large parameter and a simple turning point. These involve Airy functions, but not their derivatives, unlike traditional asymptotic expansions. From these, asymptotic expansions are derived for the zeros of Bessel functions that are valid for large positive values of the order, uniformly valid for all the zeros. The coefficients in the expansions are explicitly given elementary functions, and similar expansions are derived for the zeros of the derivatives of Bessel functions.

Cited by

• Bounds and asymptotic expansions for the radii of convexity and uniform convexity of normalized Bessel functions
• Uniform Asymptotic approximation and numerical evaluation of the Reverse Generalized Bessel Polynomial zeros
• Uniform asymptotic expansions for generalised trigonometric integrals and their zeros
• Simplified Airy function Asymptotic expansions for Reverse Generalised Bessel Polynomials

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• Uniform asymptotic expansions for Bessel functions of imaginary order and their zeros
• Simplified Airy function Asymptotic expansions for Reverse Generalised Bessel Polynomials
• Asymptotic behavior of zeros of Bessel function derivatives
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