Extended k-gamma and k-beta functions of matrix arguments

Ghazi S. Khammash; Praveen Agarwal; Junesang Choi

doi:10.3390/math8101715

Extended k-gamma and k-beta functions of matrix arguments

Ghazi S. Khammash
, Praveen Agarwal
, Junesang Choi

Al-Aqsa University
International College of Engineering
Dongguk University

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

33 Scopus citations

Abstract

Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

Original language	English
Article number	1715
Pages (from-to)	1-13
Number of pages	13
Journal	Mathematics
Volume	8
Issue number	10
DOIs	https://doi.org/10.3390/math8101715
State	Published - Oct 2020
Externally published	Yes

Keywords

Beta function of matrix arguments
Extended beta function of matrix arguments
Extended gamma function of a matrix argument
Extended k-beta function of matrix arguments
Extended k-gamma function of a matrix argument
Gamma function of a matrix argument
K-beta function
K-beta function of matrix arguments
K-gamma function
K-gamma function of a matrix argument

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10.3390/math8101715

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title = "Extended k-gamma and k-beta functions of matrix arguments",

abstract = "Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.",

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AU - Khammash, Ghazi S.

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AU - Choi, Junesang

PY - 2020/10

Y1 - 2020/10

N2 - Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

AB - Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

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KW - Extended beta function of matrix arguments

KW - Extended gamma function of a matrix argument

KW - Extended k-beta function of matrix arguments

KW - Extended k-gamma function of a matrix argument

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ER -

Extended k-gamma and k-beta functions of matrix arguments

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