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.
In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansions of the Humbert matrix polynomials of two variables in series of Hermite polynomials are given. Results of Gegenbauer matrix polynomials of two variables follow as particular cases of Humbert matrix polynomials of two variables.
The main aim of this paper is to use the integral representation method to derive the properties of Legendre polynomials. Their recurrence relations, differential equations, relationship with Hermite polynomials have been obtained.
Articles you may be interested inq 2-Kampé de Fériet series and sums of continuous dual q ±2-Hahn polynomials Abstract. The object of this paper is to drive some basic relations involving the generalization of Humbert polynomials of two variables , , n k x y 4 and then take up several operation results. Series representations, hypergeometric representations and expansions of , , n k x y 4 in series of other polynomials which are best stated in terms of generalized polynomials of two variables.
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