TITLE:
On a Unification of Generalized Mittag-Leffler Function and Family of Bessel Functions
AUTHORS:
Jyotindra C. Prajapati, Bhadresh I. Dave, Bharti V. Nathwani
KEYWORDS:
Generalized Mittag-Leffler Function; Recurrence Relation; Wiman’s Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.1,
January
29,
2013
ABSTRACT: 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.