Investigation of Integral Transformation Associated with Extended Generalized Srivastava’s Hypergeometric Multi Variable Special Function

Abstract

In recent year study on multivariate special functions and Integral transformation have been booming. In this work, we have focused on Srivastava hypergeometric function , , and  with triple variable. We have discussed the literature study and motivation from the recent works on the extension of Srivastava’s multivariable hypergeometric function , , and . In this paper, the extension of , , and  is studied based on the generalized beta  function  and the generalized Pochhammer’s symbol . Furthermore, the Mellin integral transformation and Inverse Mellin integral transformation have been studied for the  based extension of the functions , , and . A few of the most recent uses of these transformations in various scientific and engineering fields are also highlighted in this paper. In general, this work seeks to offer a thorough overview of recent breakthroughs in the importance and applications of several integral transforms of Multivariable functions.