T. M. Dunster
Published 2023-10-24Version 1
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.
On the complex zeros of Airy and Bessel functions and those of their derivatives
High-order derivatives of the Bessel functions with an application
Uniform enclosures for the phase and zeros of Bessel functions and their derivatives
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