Extended hypergeometric and confluent hypergeometric functions

摘要

An extension of the beta function by introducing an extra parameter, which proved to be useful earlier, is applied here to extend the hypergeometric and confluent hypergeometric functions. Since the latter functions contain many of the familiar special functions as sub-cases, this extension is expected to prove to be useful. The object of the present paper is to study this extension and its relationship with the hypergeometric and confluent hypergeometric functions.