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

S. A. Dar, Richard B. Paris

Research output: Contribution to journalArticle

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
Bp,v(x, y) introduced in [9]. 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 functionF1,p,v(·) involving Meijer’s G-function are obtained.
Original languageEnglish
Number of pages12
JournalJournal of Computational and Applied Mathematics
Early online date12 Mar 2019
DOIs
Publication statusE-pub ahead of print - 12 Mar 2019

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Appell Functions
Integral Representation
Recursion Formula
G-function
Transform

Cite this

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abstract = "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.",
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A (p, ν)-extension of the Appell function F1(·) and its properties. / Dar, S. A.; Paris, Richard B.

In: Journal of Computational and Applied Mathematics, 12.03.2019.

Research output: Contribution to journalArticle

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AU - Paris, Richard B.

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N2 - 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.

AB - 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.

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