An Extension of Pochhammer’s Symbol and its Application to Hypergeometric Functions

Abstract

By using a special property of the gamma function, we first define a productive form of gamma
and beta functions and study some of their general properties in order to define a new extension of the
Pochhammer symbol. We then apply this extended symbol for generalized hypergeometric series and
study the convergence problem with some illustrative examples in this sense. Finally, we introduce two
new extensions of Gauss and confluent hypergeometric series and obtain some of their general properties.