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On a Unification of Generalized Mittag-Leffler Function and Family of Bessel Functions

Author(s): Jyotindra C. Prajapati | Bhadresh I. Dave | Bharti V. Nathwani

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 01;
Start page: 127;
Date: 2013;
Original page

Keywords: Generalized Mittag-Leffler Function | Recurrence Relation | Wiman’s Function

In the present work, a unification of certain functions of mathematical physics is proposed and its properties are studied. The proposed function unifies Lommel function, Struve function, the Bessel-Maitland function and its generalization, Dotsenko function, generalized Mittag-Leffler function etc. The properties include absolute and uniform convergence, differential recurrence relation, integral representations in the form of Euler-Beta transform, Mellin-Barnes transform, Laplace transform and Whittaker transform. The special cases namely the generalized hypergeometric function, generalized Laguerre polynomial, Fox H-function etc. are also obtained.
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