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Multiple-term approximations for Appell's F1 function

Published online by Cambridge University Press:  17 February 2009

Magdi A. El-Gabali
Magdi A. El-Gabali
Affiliation:
Kuwait University, Department of Mathematics and Computer Science, P.O. Box 5969 Safat 13060, Kuwait
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Abstract

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In this paper computational issues of Appell's F1 function

are addressed. A novel technique is used in the derivation of highly efficient multiple-term approximations of this function (including asymptotic ones). Simple structured single- and double-term approximations, as the first two candidates of this multiple-term representa-tion, are developed in closed form. Error analysis shows that- the developed algorithms are superior to existing approximations for the same number of terms. The formulation presented is highly efficient and could be extended to a wide class of special functions.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 1 , July 1997 , pp. 135 - 148
Copyright
Copyright © Australian Mathematical Society 1997

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