On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals

Abstract

In this paper, we first introduce the 2-variables Konhauser matrix polynomials; then, we investigate some properties of these matrix polynomials such as generating matrix relations, integral representations, and finite sum formulae. Finally, we obtain the fractional integrals of the 2-variables Konhauser matrix polynomials.

On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial

“…Furthermore, upon using the generalized binomial expansion, we find that the inner sum in (18) yields…”

“…We say that if Re(ξ) for all ξ ∈ σ(A), a matrix A in C r×r is a positive stable matrix. In [9,[17][18][19], if f(z) and g(z) are holomorphic functions in an open set Λ of the complex plane and if A is a matrix in C r×r for which σ(A) ⊂ Λ, then f(A)g(A) � g(A)f(A).…”

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

“…In the past few decades, the orthogonal matrix polynomials have attracted a lot of research interests due to their close relations and various applications in many areas of mathematics, engineering, probability theory, graph theory and physics; for example, see [1][2][3][4][5][6][7][8][9]. In [4], extension to the matrix framework of the classical families of Legendre, Laguerre, Jacobi, Chebyshev, Gegenbaner and Hermite polynomials have been introduced.…”

Fractional order of Legendre-type matrix polynomials

“…On the contrary, the mainstream and, perhaps, the most effective approach to the field of special functions of matrix argument is the fractional calculus approach, recently presented in the fundamental works (for instance, see [16][17][18][19]). Analogous to the classical case, it is also noticed that Rodrigues matrix formula is a useful approach to define a sequence of orthogonal matrix polynomials (see [1,[20][21][22][23][24][25]).…”

“…[1,17]) Let D be a positive stable matrix in C N×N and μ ∈ C such that Re(μ) > 0, the Riemann-Liouville fractional integral of order μ is defined as follows:…”