A new Generalization of Extended Beta and Hypergeometric Functions

Kottakkaran Sooppy Nisar; Gauhar Rahman; Shahid Mubeen

doi:10.20944/preprints201802.0036.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 31 January 2018 / Approved: 5 February 2018 / Online: 5 February 2018 (14:30:15 CET)

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

Beta function; extended beta function; hypergeometric function; extended hypergeometric function; con uent hypergeometric function; extended con uent hyperge- ometric function; Mellin transform; beta distribution; transformation formula; summation formula.

Computer Science and Mathematics, Analysis

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A new Generalization of Extended Beta and Hypergeometric Functions

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