Error bounds for the asymptotic expansions of the Hermite polynomials

DOI10.1017/prm.2021.90OpenAlexW3197222074MaRDI QIDQ5888268

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

Publication date: 24 April 2023

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.01054

zbMATH Keywords

error boundsasymptotic expansionsHermite polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Uses Software

• DLMF

Cites Work

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• Asymptotische Entwicklung und Nullstellenabschätzung der Hermiteschen Funktionen
• On a uniform treatment of Darboux's method
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Asymptotic Approximations and Error Bounds
• Error Bounds for Asymptotic Expansions of Integrals
• Hyperasymptotics for integrals with saddles
• Error bounds for the method of steepest descents
• Globally Exact Asymptotics for Integrals with Arbitrary Order Saddles
• Asymptotics of linear recurrences
• The calculation of the coefficients of certain asymptotic series by means of linear recurrent relations

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