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

S. A. Dar; R. B. Paris

doi:10.1016/j.cam.2019.03.001

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

S. A. Dar^*, R. B. Paris

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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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 language	English
Pages (from-to)	12-19
Number of pages	8
Journal	Journal of Computational and Applied Mathematics
Volume	358
Early online date	12 Mar 2019
DOIs	https://doi.org/10.1016/j.cam.2019.03.001
Publication status	Published - 1 Oct 2019

Keywords

Appell’s hypergeometric functions
Beta and gamma functions
Eulerian integrals
Bessel function
Meijer’s G-function

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10.1016/j.cam.2019.03.001

Paris_A(p,v)ExtensionOfTheAppell_Accepted_2019Accepted author manuscript, 469 KBLicence: CC BY-NC-ND

Cite this

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

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{\textquoteright}s G-function are obtained.",

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AU - Dar, S. A.

AU - Paris, R. B.

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N2 - 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.

AB - 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.

U2 - 10.1016/j.cam.2019.03.001

DO - 10.1016/j.cam.2019.03.001

M3 - Article

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SP - 12

EP - 19

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

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

Abstract

Keywords

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