A NOTE ON EXTENDED BETA FUNCTION INVOLVING GENERALIZED MITTAG-LEFFLER FUNCTION AND ITS APPLICATIONS

A NOTE ON EXTENDED BETA FUNCTION INVOLVING GENERALIZED MITTAG-LEFFLER FUNCTION AND ITS APPLICATIONS

N. Khan, S. Husain

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Abstract

The main object of this paper is to introduce a new extension of beta function involving generalized Mittag-le er function and study its important properties, like integral representation, summation formula, derivative formula, beta distribution, transform formula. Using this de nition, we introduce new extended hypergeometric and con uent hypergeometric function.

Keywords

Gamma function, Beta function, Hypergeometric function, Con uent hypergeometric function, Beta Distribution