A new extension of Hermite matrix polynomials and its applications
A two-variable extension of Hermite matrix polynomials is introduced and studied. It is proved that these matrix polynomials satisfy some recurrence relations and appear as finite series solution of matrix differential equations. The two-variable Hermite matrix polynomials series expansion of \(\exp(Ax)\), \(\sin(Ax)\) and \(\cos(Ax)\) for a matrix \(A \in {\mathbb C}^{N \times N}\), that satisfies an appropriate spectral property, is given. The Rodrigues' formula of two-variable Hermite matrix polynomials is presented. Finally, by using this family of matrix polynomials the Chebyshev matrix polynomials of the second kind are defined.
scientific article; zbMATH DE number 5077729