An extension of k-hypergeometric functions

Shilpi Jain; Praveen Agarwal; Parik Laxmi

doi:10.1016/B978-0-44-336484-6.00014-X

An extension of k-hypergeometric functions

Shilpi Jain
, Praveen Agarwal
, Parik Laxmi

Nonlinear Dynamic Research Centre (NDRC)

Poornima College of Engineering
International College of Engineering
Poornima University

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

Abstract

Here, we present an extension of the k-class of hypergeometric functions by use of the two-parameter k-Mittag-Leffler function. We study many identities of these extensions like the symmetric relation, functional relation, generating relations, summation formulas, derivative formulas, integral representations, the Mellin transform, and generalizing these identities that are satisfied by the k-Gauss hypergeometric and k-confluent hypergeometric functions.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	79-106
Number of pages	28
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00014-X
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/B978-0-44-336484-6.00014-X

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AU - Agarwal, Praveen

AU - Laxmi, Parik

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N2 - Here, we present an extension of the k-class of hypergeometric functions by use of the two-parameter k-Mittag-Leffler function. We study many identities of these extensions like the symmetric relation, functional relation, generating relations, summation formulas, derivative formulas, integral representations, the Mellin transform, and generalizing these identities that are satisfied by the k-Gauss hypergeometric and k-confluent hypergeometric functions.

AB - Here, we present an extension of the k-class of hypergeometric functions by use of the two-parameter k-Mittag-Leffler function. We study many identities of these extensions like the symmetric relation, functional relation, generating relations, summation formulas, derivative formulas, integral representations, the Mellin transform, and generalizing these identities that are satisfied by the k-Gauss hypergeometric and k-confluent hypergeometric functions.

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

UR - https://www.scopus.com/pages/publications/105032934608

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SN - 9780443364853

SP - 79

EP - 106

BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

An extension of k-hypergeometric functions

Abstract

Keywords

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