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EXTENDED HYPERGEOMETRIC FUNCTIONS OF TWO AND THREE VARIABLES

  • AGARWAL, PRAVEEN (Department of Mathematics Anand International College of Engineering) ;
  • CHOI, JUNESANG (Department of Mathematics Dongguk University) ;
  • JAIN, SHILPI (Department of Mathematics Poornima College of Engineering)
  • Received : 2014.11.25
  • Published : 2015.10.31

Abstract

Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

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  1. Generating relations and multivariable Aleph-function vol.38, pp.3, 2018, https://doi.org/10.1515/anly-2017-0054