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

This chapter delves into the significant properties and integral equations associated with the second kind Chebyshev matrix polynomials in two variables. It begins by introducing the preliminaries and the importance of generalized and multivariate forms of special functions in physical mathematics. The text then focuses on the recurrence relations and differential equations satisfied by these matrix polynomials, providing detailed derivations and proofs. One of the highlights is the explicit representation of these polynomials in terms of hypergeometric matrix functions. Additionally, the chapter explores the expansions of Chebyshev matrix polynomials in series of Hermite and Laguerre matrix polynomials, offering a deeper understanding of their interconnections. The chapter concludes with the derivation of the Volterra integral equation associated with these polynomials, showcasing the practical applications of these theoretical findings. Throughout, the text emphasizes the importance of generating functions in extracting properties related to two-variable extensions of these polynomials, making it a valuable resource for specialists in the field.