A (p,ν)-extension of Srivastava's triple hypergeometric function H_ B and its properties

S. A. Dar; R. B. Paris

doi:10.1515/anly-2018-0070

A (p,ν)-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

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Abstract

In this paper, we obtain a (p, ν)-extension of Srivastava’s triple hypergeometric function H_B ⁢ (⋅), by using the extended beta function B_p_,ν ⁢ (x, y) introduced in [R. K. Parmar, P. Chopra and R. B. Paris, On an extension of extended beta and hypergeometric functions, J. Class. Anal. 11 (2017), no. 2, 91–106]. 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.

Original language	English
Pages (from-to)	113-122
Number of pages	10
Journal	Analysis (Germany)
Volume	41
Issue number	2
Early online date	20 Feb 2021
DOIs	https://doi.org/10.1515/anly-2018-0070
Publication status	Published - 1 May 2021

Keywords

Srivastava's triple hypergeometric functions
Beta and gamma functions
Exton's triple hypergeometric function
Bessel function
Bounded inequality

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10.1515/anly-2018-0070

Paris_A(p,v)-ExtensionOfSrivastava'sTripleHypergeometricFunction_Accepted_2021Accepted author manuscript, 448 KB

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abstract = "In this paper, we obtain a (p, ν)-extension of Srivastava{\textquoteright}s triple hypergeometric function HB ⁢ (⋅), by using the extended beta function Bp,ν ⁢ (x, y) introduced in [R. K. Parmar, P. Chopra and R. B. Paris, On an extension of extended beta and hypergeometric functions, J. Class. Anal. 11 (2017), no. 2, 91–106]. We give some of the main properties of this extended function, which include several integral representations involving Exton{\textquoteright}s hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality.",

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AU - Dar, S. A.

AU - Paris, R. B.

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N2 - In this paper, we obtain a (p, ν)-extension of Srivastava’s triple hypergeometric function HB ⁢ (⋅), by using the extended beta function Bp,ν ⁢ (x, y) introduced in [R. K. Parmar, P. Chopra and R. B. Paris, On an extension of extended beta and hypergeometric functions, J. Class. Anal. 11 (2017), no. 2, 91–106]. 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.

AB - In this paper, we obtain a (p, ν)-extension of Srivastava’s triple hypergeometric function HB ⁢ (⋅), by using the extended beta function Bp,ν ⁢ (x, y) introduced in [R. K. Parmar, P. Chopra and R. B. Paris, On an extension of extended beta and hypergeometric functions, J. Class. Anal. 11 (2017), no. 2, 91–106]. 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.

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EP - 122

JO - Analysis (Germany)

JF - Analysis (Germany)

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ER -

A (p,ν)-extension of Srivastava's triple hypergeometric function H_ B and its properties

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Keywords

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