Approximation of Mathieu functions by parabolic cylinder functions

DOI10.1134/s0001434623090031zbMath1527.34052OpenAlexW4387902516MaRDI QIDQ6084892

E. A. Zlobina

Publication date: 7 November 2023

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434623090031

zbMATH Keywords

Mathieu equationasymptoticsparabolic cylinder function

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Asymptotic properties of solutions to ordinary differential equations (34D05) Lamé, Mathieu, and spheroidal wave functions (33E10)

Cites Work

• Uniform asymptotic approximation of Mathieu functions
• Mathieu functions of general order: connection formulae, base functions and asymptotic formulae. I. Introduction
• The Solutions of the Mathieu Equation with a Complex Variable and at Least One Parameter Large
• UNIFORM ASYMPTOTIC FORMS OF MODIFIED MATHIEU FUNCTIONS
• Uniform asypmptotic expansions of modified Mathieu functions.
• The Solutions of Second Order Linear Ordinary Differential Equations About a Turning Point of Order Two
• Global asymptotics for functions of parabolic cylinder and solutions of the Schrödinger equation with a potential in the form of a nonsmooth double well
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