HERMITE MATRIX POLYNOMIALS AND SECOND ORDER MATRIX DIFFERENTIAL EQUATIONS

InthispaperweintroducetheclassofHermite’smatrixpolynomialswhichappearasfiniteseriessolutionsofsecondordermatrixdifferentialequationsY"-xAY’+BY=0.AnexplicitexpressionfortheHermitematrixpolynomials,theorthogonalitypropertyandaRodrigues’formulaaregiven.