A (p, ν)-extension of the Appell function F1(·) and its properties

In this paper, we obtain a (p, v)-extension of the Appell hypergeometric functionF1(·), together with its integral representation, by using the extended Beta functionBp,v(x, y) introduced in [9]. Also, we give some of its main properties, namely theMellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, some new integral representations of the extended Appell functionF1,p,v(·) involving Meijer’s G-function are obtained