Solutions at infinity of the generalized matrix-valued hypergeometric equation

The purpose of this paper is to study the generalized matrix-valued hypergeometric equation at infinity. This equation is obtained by extending the number of parameters of the matrix-valued analog of Euler’s hypergeometric differential equation, introduced by J. Tirao (2003) in [3]. We describe the solutions of the generalized hypergeometric equation at z = ∞ in terms of matrix-valued generalized hypergeometric functions n F m .