Preprint Article Version 1 This version is not peer-reviewed

# A New Representation of Extended Mittage-Leffler Function and Its Properties

Version 1 : Received: 14 April 2019 / Approved: 16 April 2019 / Online: 16 April 2019 (10:36:23 CEST)

How to cite: Ghaffar, A.; Saif, A.; Khan, F. A New Representation of Extended Mittage-Leffler Function and Its Properties. Preprints 2019, 2019040179 (doi: 10.20944/preprints201904.0179.v1). Ghaffar, A.; Saif, A.; Khan, F. A New Representation of Extended Mittage-Leffler Function and Its Properties. Preprints 2019, 2019040179 (doi: 10.20944/preprints201904.0179.v1).

## Abstract

In this article, our main purpose is to establish a new extension of Mittag-Leffler function by using the known extended beta function $\mathbf{B}_{\omega}(a,b;p)$ introduced in [1]. It led to a novel extension of the applicability of Mittag-Leffler function that introduced them as distributions defined for a specific set of functions. We also, investigate some of its important properties, namely recursion relation, Mellin transform and differential formulas.

## Subject Areas

Mittag-Leffler function; extended Mittag-Leffler function; Extended beta function; Fox Wright function

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