Certain Properties and Their Volterra Integral Equation Associated with the Second Kind Chebyshev Matrix Polynomials in Two Variables

Abstract

AbstractThis paper presents several properties associated with the two-variable extension of the Chebyshev matrix polynomials of the second kind. In particular, we establish a three-term recurrence relation for these two-variable matrix polynomials and show that these two-variable matrix polynomials satisfy some second-order matrix differential equations. We derive their hypergeometric matrix representation and an expansion formula which links these generalized Chebyshev matrix polynomials with the Hermite matrix polynomials and the Laguerre matrix polynomials. We also drive their Volterra integral equation.KeywordsHermiteLaguerre and Chebyshev matrix polynomialsHypergeometric matrix functionsMatrix recurrence relationsDifferential equationsVolterra integral equation