Uniform asymptotic expansions for Lommel, Anger-Weber and Struve functions

2021/04/04 by T. M. Dunster, Dunster, T. M.
Computer Science · Mathematics · #33C10 #34E05 #34E20 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2104.01700

openalex publication_date 2021/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a differential equation approach asymptotic expansions are rigorously obtained for Lommel, Weber, Anger-Weber and Struve functions, as well as Neumann polynomials, each of which is a solution of an inhomogeneous Bessel equation. The approximations involve Airy and Scorer functions, and are uniformly valid for large real order ν and unbounded complex argument z. An interesting complication is the identification of the Lommel functions with the new asymptotic solutions, and in order to do so it is necessary to consider certain sectors of the complex plane, as well as introduce new forms of Lommel and Struve functions.

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