Generalized q-Mittag-Leffler function and its properties.

• B. V. Nathwani Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390 002.

Keywords: q -Mittag-Leffler function, q-Bessel function, q-difference equation, q-inverse series, eigen function, generalized q-Konhauser polynomial, series inequality relations

Abstract

Motivated essentially by the success of the applications of the Mittag-Leffler functions in Science and Engineering, we propose here a unification of certain q-extensions of generalizations of Mittag-Leffler function together with Saxena-Nishimoto's function, Bessel-Maitland function, Dotsenko function, Elliptic Function, etc. We obtain Mellin-Barnes contour integral representation, a q-difference equation, Eigen function property. As a specialization, a generalization of q-Konhauser polynomial is considered for which the series inequality relations and inverse series relations are obtained.

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