A $(p,\nu)$-extension of the Appell function $F_1(\cdot)$ and its properties

S A Dar; R B Paris

A $(p,\nu)$-extension of the Appell function $F_1(\cdot)$ and its properties

Classical Analysis and ODEs 2017-11-29 v1

Authors: S A Dar , R B Paris

Abstract

In this paper, we obtain a $(p,v)$ -extension of the Appell hypergeometric function $F_{1}(\cdot)$ , 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 $F_{1,p,v}(\cdot)$ involving Meijer's $G$ -function are obtained.

Keywords

appell hypergeometric function extended beta function integral representation mellin transform recursion formulas meijer g-function

Cite

@article{arxiv.1711.07780,
  title  = {A $(p,\nu)$-extension of the Appell function $F_1(\cdot)$ and its properties},
  author = {S A Dar and R B Paris},
  journal= {arXiv preprint arXiv:1711.07780},
  year   = {2017}
}

Comments

11 pages, 0 figures. arXiv admin note: text overlap with arXiv:1711.07809

A $(p,\nu)$-extension of the Appell function $F_1(\cdot)$ and its properties

Abstract

Keywords

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