A (p,q)-extension of Srivastava's triple hypergeometric function HB and its properties

S. A. Dar; R. B. Paris

doi:10.1016/j.cam.2018.08.045

A (p,q)-extension of Srivastava's triple hypergeometric function H_B and its properties

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

^*Corresponding author for this work

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

5 Citations (Scopus)

148 Downloads (Pure)

Abstract

In this paper, we obtain a (p,q)-extension of Srivastava's triple hypergeometric function H_B(⋅), by using the extended Beta function B_p,q(x,y) introduced by Choi et al. (2014). We give some of the main properties of this extended function, which include several integral representations involving Exton's hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, a new integral representation of the extended Srivastava triple hypergeometric function involving Laguerre polynomials is obtained.

Original language	English
Pages (from-to)	237-245
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	348
Early online date	5 Sep 2018
DOIs	https://doi.org/10.1016/j.cam.2018.08.045
Publication status	Published - 1 Mar 2019

Keywords

Srivastava’s triple hypergeometric functions
Appell’s hypergeometric functions
Exton’s triple hypergeometric functions
Beta and Gamma functions
Laguerre polynomials
Eulerian integrals
Gauss hypergeometric function

Access to Document

10.1016/j.cam.2018.08.045

Paris_A(p; q)-extensionOfSrivastava's_Accepted_2018Accepted author manuscript, 376 KBLicence: CC BY-NC-ND

Cite this

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abstract = "In this paper, we obtain a (p,q)-extension of Srivastava's triple hypergeometric function HB(⋅), by using the extended Beta function Bp,q(x,y) introduced by Choi et al. (2014). We give some of the main properties of this extended function, which include several integral representations involving Exton's hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, a new integral representation of the extended Srivastava triple hypergeometric function involving Laguerre polynomials is 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,q)-extension of Srivastava's triple hypergeometric function HB(⋅), by using the extended Beta function Bp,q(x,y) introduced by Choi et al. (2014). We give some of the main properties of this extended function, which include several integral representations involving Exton's hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, a new integral representation of the extended Srivastava triple hypergeometric function involving Laguerre polynomials is obtained.

AB - In this paper, we obtain a (p,q)-extension of Srivastava's triple hypergeometric function HB(⋅), by using the extended Beta function Bp,q(x,y) introduced by Choi et al. (2014). We give some of the main properties of this extended function, which include several integral representations involving Exton's hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, a new integral representation of the extended Srivastava triple hypergeometric function involving Laguerre polynomials is obtained.

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DO - 10.1016/j.cam.2018.08.045

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JO - Journal of Computational and Applied Mathematics

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