Asymptotic solutions of inhomogeneous differential equations having a turning point

2020/05/17 by T. M. Dunster, Dunster, T. M.
Mathematics · Physics and Astronomy · #33C10 #34E05 #34E20 #Classical Analysis and ODEs (math.CA) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Mathematical functions and polynomials #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2005.08152

openalex publication_date 2020/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The asymptotic approximations are uniformly valid for unbounded complex values of the argument, and are applied to inhomogeneous Airy equations having polynomial and exponential forcing terms. Error bounds are available for all approximations, including new simple ones for the well-known asymptotic expansions of Scorer functions of large complex argument.

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