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In the present research note, we define a new extension of beta function by making use of the multi-index Mittag-Leffler function. Here, first we derive its fundamental properties and then we present a new type of beta distribution as an application of our proposed beta function. Moreover, we present a new extension of Gauss and confluent hypergeometric functions in terms of our newly introduced beta function. Some interesting properties of our extended hypergeometric functions (like integral representations, differential formulae, transformations and summation formulae and a generating relation) are also indicated in the last section. AMS Subject Classification: 33B15, 33B20, 33C05, 33C15, 33E12

A STUDY OF EXTENDED BETA, GAUSS AND CONFLUENT HYPERGEOMETRIC FUNCTIONS