Title

Generalized elliptic-type integrals and their representations

Authors

Authors

M. Salman

Comments

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Abbreviated Journal Title

Appl. Math. Comput.

Keywords

elliptic-type integrals; hypergeometric functions; Mathematics, Applied

Abstract

Epstein-Hubbell [L.F. Epstein, J.H. Hubbell, Evaluation of a generalized elliptic-type integral, J. Res. NBS 67B (1963) 1-17] elliptic-type integrals occur in radiation field problems. In this paper, we consider a generalization (10) of the elliptic-type integrals introduced by Kalla and Tuan [S.L. Kalla, Vu Kim Tuan, Asymptotic formulas for generalized elliptic-type integrals, Comput. Math. Appl. 32 (1996) 49-55]. Many generalizations of elliptic-type integrals, studied earlier by several authors, can be derived as particular cases of our unified form. We study the uniform convergence of the integral representation (10). We derive the power series representations which are valid in different domains. Also we obtain some relationships between this generalized form and Laurecella's hypergeometric function of three variables F-D((3)), Appell's hypergeometric functions F-1 and F-3 and Gauss' hypergeometric function F-2(1). Some important particular Cases of these representations are derived. (c) 2006 Elsevier Inc. All rights reserved.

Journal Title

Applied Mathematics and Computation

Volume

181

Issue/Number

2

Publication Date

1-1-2006

Document Type

Article

Language

English

First Page

1249

Last Page

1256

WOS Identifier

WOS:000242385400047

ISSN

0096-3003

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