Timour Sadykov, Stockholm University, Sweden
e-mail: timur@matematik.su.se

Special functions of hypergeometric type and a basis in the solution space of the Horn system of equations

Abstract

We study the approach to the theory of special functions of hypergeometric type in several variables via a generalization of the Horn system of differential equations. A formula for the dimension of its solution space is given. Using this formula we construct a basis in the space of holomorphic solutions to the generalized Horn system under some assumptions on its parameters.