Abstract
In this paper, we obtain a ( p , v ) -extension of the Appell hypergeometric function F 1 ( ⋅ ) , together with its integral representation, by using the extended Beta function B p , v ( x , y ) introduced in Parmar et al. (2015). Also, we give some of its main properties, namely the Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, some new integral representations of the extended Appell function F 1 , p , v ( ⋅ ) involving Meijer’s G -function are obtained.
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