Error bounds for the asymptotic expansions of the Hermite polynomials

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

1 Scopus Citations
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Author(s)

  • Wei Shi
  • Gergő Nemes
  • Xiang-Sheng Wang
  • Roderick Wong

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)417-440
Journal / PublicationProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume153
Issue number2
Online published26 Jan 2022
Publication statusPublished - Apr 2023

Abstract

In this paper, we present explicit and computable error bounds for the asymptotic expansions of the Hermite polynomials with Plancherel-Rotach scale. Three cases, depending on whether the scaled variable lies in the outer or oscillatory interval, or it is the turning point, are considered separately. We introduce the 'branch cut' technique to express the error terms as integrals on the contour taken as the one-sided limit of curves approaching the branch cut. This new technique enables us to derive simple error bounds in terms of elementary functions. We also provide recursive procedures for the computation of the coefficients appearing in the asymptotic expansions. © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

Research Area(s)

  • asymptotic expansions, Error bounds, Hermite polynomials

Citation Format(s)

Error bounds for the asymptotic expansions of the Hermite polynomials. / Shi, Wei; Nemes, Gergő; Wang, Xiang-Sheng et al.
In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 153, No. 2, 04.2023, p. 417-440.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review