Parabolic Cylinder Functions: Examples of Error Bounds For Asymptotic Expansions

2002/05/06 by Raimundas Vidūnas, Raimundas Vidunas, Nico M. Temme +3
Computer Science · Engineering · Mathematics · #30E15 #33C10 #33F05 #41A60 (Primary) 33C15 #65D20 (Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #math.CA #msc:30E15 #msc:33C10 #msc:33C15 #msc:33F05 #msc:41A60 #msc:65D20

paper · pdf · doi:10.48550/arxiv.math/0205045

22 pages, 4 figures

arxiv created 2002/05/06 · openalex publication_date 2002/05/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincaré-type expansions for large values of the argument z and uniform expansions for large values of the parameter are considered. The expansions are based on those given in Olver(1959) and on modifications of these expansions given in Temme(2000). Computer algebra techniques are used for obtaining representations of the bounds and for numerical computations.

Related

• Numerical and Asymptotic Aspects of Parabolic Cylinder Functions
• Computation of parabolic cylinder functions having complex argument
• Uniform asymptotic expansions for the zeros of parabolic cylinder functions
• Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations
• Exponentially small expansions related to the parabolic cylinder function