A certain generalized Pochhammer symbol and its applications to hypergeometric functions

摘要

In this article, we first introduce an interesting new generalization of the familiar Pochhammer symbol by means of a certain one-parameter family of generalized gamma functions. With the help of this new generalized Pochhammer symbol, we then introduce an extension of the generalized hypergeometric function with r numerator and s denominator parameters. Finally, we present a systematic study of the various fundamental properties of the class of the generalized hypergeometric functions introduced here.