## On Laguerre matrix polynomials.(English)Zbl 0990.33008

Summary: In this paper generalized hypergeometric matrix functions are introduced. Properties of Laguerre matrix polynomials and their connections with hypergeometric and Bessel matrix functions are established. Formulas for the generating functions of products of Laguerre matrix polynomials extending well-known formulas for the scalar Laguerre polynomials are given.

### MSC:

 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 33C10 Bessel and Airy functions, cylinder functions, $${}_0F_1$$ 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable