Generalized elliptic-type integrals and their representations

    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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