Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1046.33004
Dunster, T.M.
Uniform asymptotic approximations for the Whittaker functions $M\sb {\kappa,i\mu}(z)$ and $W\sb{\kappa,i\mu}(z)$. (English)
[J] Anal. Appl., Singap. 1, No. 2, 199-212 (2003). ISSN 0219-5305

Uniform asymptotic approximations are obtained for the Whittaker's confluent hypergeometric functions $M_{\kappa,i\mu}(z)$ and $W_{\kappa,i\mu}(z)$, where $\kappa$, $\mu$ and $z$ are real. Three cases are considered, and when taken together, result in approximations which are valid for $\kappa\to\infty$ uniformly or $0\le\mu< \infty$, $0< z<\infty$, and also for $\mu\to\infty$ uniformly for $0\le\kappa<\infty$, $0< z<\infty$. The results are obtained by an application of general asymptotic theories for differential equations either having a coalescing turning point and double pole with complex exponent, or a fixed simple turning point. The resulting approximations achieve a uniform reduction of free variables from three to two, and involve either modified Bessel functions or Airy functions. Explicit error bounds are available for all the approximations.
[Francisco Perez Acosta (La Laguna)]

MSC 2000:: *33C15 Confluent hypergeometric functions
33C10 Cylinder functions, etc.
34E20 Asymptotic singular perturbations, methods (ODE)
41A30 Approximation by other special function classes

Keywords: uniform asymptotic approximation; confluent hyper-geometric functions

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