Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0835.33014
Dunster, T.M.
Uniform asymptotic approximation of Mathieu functions. (English)
[J] Methods Appl. Anal. 1, No.2, 143-168 (1994). ISSN 1073-2772

Uniform asymptotic approximations are derived for solutions of Mathieu's equation $w'' = \{2q \cos (2z) - a\} w$ for $z$ complex, and $q$ and $a$ real, $q \to \infty$. The approximations are uniformly valid for $- 2q \le a \le (2 - d)q$, where $d$ is an arbitrarily small positive constant. The approximations involve both elementary functions and Whittaker functions. Error bounds are included or available for all approximations. The paper also gives an introduction to well-known basic properties of Mathieu's equation and its solutions, which are relevant to the paper.
[N.M.Temme (Amsterdam)]

MSC 2000:: *33E10 Spheroidal wave functions, etc.
41A60 Asymptotic problems in approximation
34B30 Special ODE
34E20 Asymptotic singular perturbations, methods (ODE)

Keywords: Mathieu functions; turning point theory; asymptotic approximations; Mathieu's equation

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]