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.

Keywords

• k-gamma function
• k-beta function
• gamma function of a matrix argument
• beta function of matrix arguments
• extended gamma function of a matrix argument
• extended beta function of matrix arguments