On Matrix Polynomials Associated With Humbert Polynomials

Abstract

Abstract. The principal object of this paper is to study a class of matrix polynomials associated with Humbert polynomials. These polynomials generalize the well known class of Gegenbauer, Legendre, Pincherl, Horadam, Horadam-Pethe and Kinney polynomials. We shall give some basic relations involving the Humbert matrix polynomials and then take up several generating functions, hypergeometric representations and expansions in series of matrix polynomials.

A Class of Laguerre-Based Generalized Humbert Polynomials

“…In this section of the paper, we have derived few differentialrecursive relations involving the Laguerre-based generalized Humbert polynomial in (16), generalized class of Humbert polynomials in (13), and Hermite-Laguerre polynomial in (15).…”

Some expansions for a class of generalized Humbert matrix polynomials

“…Choosing the parameters b = 0 = y, a = m and c = −d = 1 in Theorem 2, we get the matrix representation (see [23]):…”

“…S ν n (x) is an interesting generalization of Shrestha polynomial S n (x) (see [31]). Recently, Pathan et al [23] studied a class of matrix polynomials associated with Humbert polynomials as an extension to the matrix framework of the classical families for the above mentioned polynomials by the relation…”

A note on two variable Laguerre matrix polynomials

“…Further, matrix polynomials seen in the study of many area such as statistics, Lie group theory and number theory are well known. Recently, the matrix versions of the classical families orthogonal polynomials such as Laguerre, Jacobi, Hermite, Gegenbauer, Bessel and Humbert polynomials and some other polynomials were introduced by many authors for matrices in C NÂN and various properties satisfied by them were given from the scalar case, see for example (Aktas et al, 2013;Aktas et al, 2011;Cekim, 2012a,b, 2013;Bin-Saad and Antar, 2015;Cekim and Erkus-Duman, 2014;Jo´dar and Corte´s, 1998a,b;Jo´dar and Company, 1996;Jo´dar et al, 1995;Pathan et al, 2014;Bayram and Altin, 2015).…”