APM  Vol.3 No.1 , January 2013
On a Unification of Generalized Mittag-Leffler Function and Family of Bessel Functions

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.

Cite this paper: J. Prajapati, B. Dave and B. Nathwani, "On a Unification of Generalized Mittag-Leffler Function and Family of Bessel Functions," Advances in Pure Mathematics, Vol. 3 No. 1, 2013, pp. 127-137. doi: 10.4236/apm.2013.31017.

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