The generalized matrix valued hypergeometric equation

P. ROMÁN; S. SIMONDI

INTERNATIONAL JOURNAL OF MATHEMATICS

World Scientific Publishing Company

Año: 2009 vol. 21 p. 145 - 155

0129-167X

The matrix valued analog of the Euler?s hypergeometric differential equation was introduced by Tirao in [1]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao?s equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in [1] to identify the corresponding matrix hypergeometric functions nFm. We prove that, if n = m+ 1, this functions are analytic for |z| < 1 and we give a necesary condition for the convergence on the unit circle |z| = 1.