  The matrix valued analog of the Euler's hypergeometric differential equation
was introduced by Tirao in \cite{T2}. 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 \cite{T2} to identify the corresponding matrix hypergeometric
functions ${}_nF_m$. 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.
