Quasi-monomiality and operational identities for Laguerre–Konhauser-type matrix polynomials and their applications

Abstract

Abstract. It is shown that an appropriate combination of methods, relevant to matrix polynomials and to operational calculus can be a very useful tool to establish and treat a new class of matrix LaguerreKonhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Laguerre-Konhauser matrix polynomials and discuss the links with classical polynomials.

On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals

“…In the past few years, the extension of the classical Konhauser polynomials to the Konhauser matrix polynomials of one variable has been a subject of intensive studies [11][12][13][14]. Recently, many authors (see, e.g., [15][16][17][18]) have proposed the generating relations of Konhauser matrix polynomials of one variable from the Lie algebra method point of view and found some properties of Konhauser matrix polynomials of one variable via the Lie algebra technique; they also obtained operational identities for Laguerre-Konhauser-type matrix polynomials and their applications for the matrix framework.…”