On a Kummer-type transformation for the generalized hypergeometric function 2F2

Generating Kummer Type Formulas for Hypergeometric Functions

Kummer type formulas are identities of hypergeometric series. A symmetry by the permutations of n-letters yields these formulas. We will present an algorithmic method to derive known and new Kummer type formulas. The algorithm utilizes several algorithms in algebra and geometry for generating Kummer type formulas.

Euler-type transformations for the generalized hypergeometric function

Abstract We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2Fr+1(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula...

On Integral Operator Involving Generalized Hypergeometric Function

Due to rigorous work on integral operators and the hypergeomet-ric functions, we define here an integral operator involving generalized hypergeometric function. By means of this generalized function, we introduce new classes of analytic functions and study their properties. 1 Introduction and preliminaries. Let H be the class of functions analytic in U := {z ∈ C : |z| < 1} and A be the subclass...

On Hypergeometric-type Generating Relations Associated with the Generalized Zeta Function

An Extended Gamma Function Involving a Generalized Hypergeometric Function

The objective of this paper is to define and study new generalized extended gamma functions. A generalized extended gamma probability density function involving generalized hypergeometric function is also defined. Closed form representations of the generalized gamma functions and the moment generating function are derived in the form of H-function using inverse Mellon transform techniques. Inco...