Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1153.65026
Schmelzer, Thomas; Trefethen, Lloyd N.
Computing the gamma function using contour integrals and rational approximations. (English)
[J] SIAM J. Numer. Anal. 45, No. 2, 558-571 (2007). ISSN 0036-1429; ISSN 1095-7170/e

In general, the best methods for computing the gamma function are based on the evolution of Hankel's contour integrals. In this paper, two types of generic related methods are investigated to evaluate the gamma functions with geometric accuracy. Firstly, the application of the trapezoid rule on Talbot-type contours using optimal parameters derived by {\it J.A.C. Weideman} [SIAM J. Numer. Anal. 44, No. 6, 2342-2362 (2006; Zbl 1131.65105)] for computing inverse Laplace transforms. Following {\it W. J. Cody}, {\it G. Meinardus} and {\it R. S. Varga} [J. Approximation Theory 2, 50--65 (1969; Zbl 0187.11602)], the authors also investigate quadrature formulas derived from best approximation to $\exp(z)$ on the negative real axis. The two methods are closely related, and both converge geometrically. These are competitive with existing ones, even though they are based on generic tools rather than on specific analysis of the gamma function.\par It is interesting that the second method is about twice as fast as the first, however, the first is simpler to implement as the construction of the best rational approximation is not trivial.
[C. L. Parihar (Indore)]

MSC 2000:: *65D20 Computation of special functions
33F05 Numerical approximation of special functions
33B15 Gamma-functions, etc.

Keywords: gamma function; Hankel contour; inverse Laplace transform; numerical quadrature; Talbot-type contour

Citations: Zbl 0187.11602; Zbl 1131.65105

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]