Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1048.33005
Olde Daalhuis, A.B.
Uniform asymptotic expansions for hypergeometric functions with large parameters. II. (English)
[J] Anal. Appl., Singap. 1, No. 1, 121-128 (2003). ISSN 0219-5305

An asymptotic expansion is given of the Gauss hypergeometric function ${}_2F_1(a+\lambda,b+2\lambda; c;-z)$ as $|\lambda|\to\infty$. The expansion holds for fixed values of $a$, $b$ and $c$, and holds uniformly with respect to $z$ in the domain $|\text{ph}\,z|<\pi$. The main approximant is an Airy function. The result is obtained from an integral representation. A proof about the remainder in the expansion is similar as in cited references. For Part I, see Zbl 1048.33004.
[N. M. Temme (Amsterdam)]

MSC 2000:: *33C05 Classical hypergeometric functions
34E05 Asymptotic expansions (ODE)
41A60 Asymptotic problems in approximation

Keywords: Coalescing saddles; Hypergeometric function; large parameter; Airy function; uniform asymptotic expansions

Citations: Zbl 1048.33004

Cited in: Zbl 1190.33002

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]