Work

Uniform Asymptotic Expansions for the Zeros of Parabolic Cylinder Functions

Year: 2024

Type: article

Abstract: ABSTRACT The real and complex zeros of the parabolic cylinder function are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for positive or negative and large in absolute value, uniformly for unbounded (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.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.70004

Authors: T. M. Dunster, Amparo Gil, Diego Ruiz‐Antolin, Javier Segura

Institutions: San Diego State University, Universidad de Cantabria

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministerio de Economía y Competitividad, Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación