Uniform Asymptotic Expansions for the Zeros of Parabolic Cylinder Functions

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2024-12-30 DOI:10.1111/sapm.70004

T. M. Dunster, Amparo Gil, Diego Ruiz-Antolin, Javier Segura

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引用次数: 0

Abstract

The real and complex zeros of the parabolic cylinder function $U (a, z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in absolute value, uniformly for unbounded $z$ (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function.

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.