Title: Some relations satisfied by Hermite-Hermite matrix polynomials
Abstract:The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008).Our goal is to derive their basic properties including the orthogonality properti...The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008).Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula.Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials.We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials.Finally, we establish general families and several new results concerning generalized Hermite-Hermite matrix polynomials.Read More