New Generalized Hypergeometric Functions

Abstract

The classical Gauss hypergeometric function2F1(α, β,ɤ;z) and the Kumar confluent hypergeometric function1F1(α, β,ɤ;z) are defined using a classical Pochammer symbol and a factorial function. This research paper will present (α)n a two-parameter Pochhammer symbol (λ,µ)n and discuss some of its properties such as recursive formulae and integral representation. In addition, the generalized Gauss and Kumar confluent hypergeometric functions are defined using the two-parameter Pochhammer symbol and a two-parameter factorial function (m, j)! and some of the properties of the new generalized hypergeometric functions were also discussed.