On A Matrix Hypergeometric Differential Equation

Abstract

In this paper we consider a matrix Hypergeometric differential equation, which are special matrix functions and solution of a specific second order linear differential equation. The aim of this work is to extend a well known theorem on Hypergeometric function in the complex plane to a matrix version, and we show that the asymptotic expansions of Hypergeometric function in the complex plane ” that are given in the literature are special members of our main result. Background and motivation are discussed.

Keywords

• special functions.
• a matrix hypergeometric differential equation.
• matrix
• gamma function.
• jordan canonical form.