The generalized k-hypergeometric function as the Meijer G-function

Shilpi Jain; Parik Laxmi; Praveen Agarwal

doi:10.1016/B978-0-44-336484-6.00009-6

The generalized k-hypergeometric function as the Meijer G-function

Shilpi Jain
, Parik Laxmi
, Praveen Agarwal

Nonlinear Dynamic Research Centre (NDRC)

Poornima College of Engineering
Poornima University
International College of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this chapter, we use the representation of the generalized k-hypergeometric function Fq,kp in terms of the known Meijer G-function to extend the range of parameters of such a special function so it is convergent. Also, we establish the corresponding series representation for such an extension. In particular, we extend the hypergeometric function F1,k2 and F2,k3 from |z|<1 to |z|>1.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	1-12
Number of pages	12
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00009-6
State	Published - 1 Jan 2026

Keywords

Classical beta function
Classical gamma function
Pochhammer symbol
k-Gauss hypergeometric function
k-Pochhammer symbol
k-beta function
k-confluent hypergeometric function
k-gamma function

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10.1016/B978-0-44-336484-6.00009-6

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AU - Agarwal, Praveen

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N2 - In this chapter, we use the representation of the generalized k-hypergeometric function Fq,kp in terms of the known Meijer G-function to extend the range of parameters of such a special function so it is convergent. Also, we establish the corresponding series representation for such an extension. In particular, we extend the hypergeometric function F1,k2 and F2,k3 from |z|<1 to |z|>1.

AB - In this chapter, we use the representation of the generalized k-hypergeometric function Fq,kp in terms of the known Meijer G-function to extend the range of parameters of such a special function so it is convergent. Also, we establish the corresponding series representation for such an extension. In particular, we extend the hypergeometric function F1,k2 and F2,k3 from |z|<1 to |z|>1.

KW - Classical beta function

KW - Classical gamma function

KW - Pochhammer symbol

KW - k-Gauss hypergeometric function

KW - k-Pochhammer symbol

KW - k-beta function

KW - k-confluent hypergeometric function

KW - k-gamma function

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SN - 9780443364853

SP - 1

EP - 12

BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

The generalized k-hypergeometric function as the Meijer G-function

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Keywords

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