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

2017/11/21 by Dar, S A, Paris, R B
#33B15 #33C10 #33C45 #33C60 #33C65 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.07780

Abstract

In this paper, we obtain a (p,v)-extension of the Appell hypergeometric function F₁(⋅), together with its integral representation, by using the extended Beta function B_p,v(x,y) introduced in arXiv:1502.06200. 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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