Hermite–Laguerre Matrix Polynomials and Generating Relations

The Hermite–Laguerre matrix polynomials and the Hermite-modified Laguerre matrix polynomials are introduced. Certain generating relations for the Hermite–Laguerre matrix polynomials are derived by using operational methods. Some results for the matrix and scalar special polynomials related to these new special matrix polynomials are also obtained as applications.