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

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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

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

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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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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

M3 - Article

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -

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

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