Certain properties of modified Hermite-type matrix polynomials

Abstract

This paper deals with the investigation of an expansion formula, a summation formula, a multiplication theorem, an addition theorem, matrix recurrence relations, fractional integrals, fractional derivatives, Laplace transform, Mellin transform and Fractional Fourier transform for the modified Hermite-type matrix polynomials and some other properties. We also give new definitions for the modified Chebyshev’s-type, the modified Legendre’s-type and the modified Hermite-Hermite-type matrix polynomials by using these polynomials and we further prove some new results and relations.