References & Citations
Mathematics > Classical Analysis and ODEs
Title: Uniform asymptotic expansions for the zeros of Bessel functions
(Submitted on 24 Oct 2023 (v1), last revised 13 May 2024 (this version, v3))
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.
Submission history
From: T. M. Dunster [view email][v1] Tue, 24 Oct 2023 17:21:38 GMT (508kb)
[v2] Fri, 24 Nov 2023 21:04:17 GMT (508kb)
[v3] Mon, 13 May 2024 20:50:02 GMT (509kb)
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