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.
Highlights
We propose an extension of a generalization of the Mittag-Leffler function due to A
It is noteworthy that the function in (1.2), besides containing the generalizations of the Mittag-Leffler function, includes certain functions belonging to the family of Bessel function
(1.2), we find the well known Bessel function [8]: J
Summary
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. We propose an extension of a generalization of the Mittag-Leffler function due to A. (1.1) contains the E z -Mittag-Leffler function [2], E , z - The generalized Mittag-Leffler function [3] and the function E , z due to Prabhakar [4].
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