Some Remarks on Extended Hypergeometric, Extended Confluent Hypergeometric and Extended Appell's Functions

Abstract

Recently, Chaudhry et al. have introduced the extended hypergeometric functions (EHF) and extended confluent hypergeometric functions (ECHF) by using the generalized beta functions [1]. In a similar way, Ozarslan et al. extended the first two Appell's hypergeometric functions. In this paper, we show that these extended functions can be represented in terms of a finite number of well known higher transcendental functions, especially as an infinite series containing hypergeometric, confluent hy-pergeometric, Whittaker's, Lagrange functions, Laguerre polynomials, and products of them.