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Uniform asymptotic expansions for Lommel, Anger‐Weber, and Struve functions
Author(s) -
Dunster T. M.
Publication year - 2022
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12442
Subject(s) - mathematics , bessel function , mathematical analysis , struve function , airy function , differential equation , orthogonal polynomials , gegenbauer polynomials , classical orthogonal polynomials
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.