Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1013.65017
MacLeod, Allan J.
The efficient computation of some generalised exponential integrals. (English)
[J] J. Comput. Appl. Math. 148, No.2, 363-374 (2002). ISSN 0377-0427

Summary: The accurate and efficient computation of the special functions $G_k(x)$ is discussed, where $$G_k(x)=\frac{1}{(k-1)!}\int^\infty_1\exp(-xy)(\log y)^{k-1}\frac{dy}{y} .$$ These functions appear in the computation of the derivatives of the L-series of an elliptic curve, and in radiative transfer problems from astrophysics. By dividing $(0,\infty)$ into 3 sub-intervals, we derive Chebyshev polynomial expansions for $Gk$, $k=1,\dots,4$ with the coefficients given to an accuracy of 20 decimal places.

MSC 2000:: *65D20 Computation of special functions
33C60 Hypergeometric integrals and functions defined by them
33F05 Numerical approximation of special functions

Keywords: Chebyshev expansion; generalised exponential integrals; elliptic curves; Meijer's $G$-function

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]