The basic Gauss hypergeometric matrix function and its matrix q-difference equation - Salem, Ahmed (Linear & multilinear algebra, 2014)
In this paper, the basic Gauss hypergeometric matrix function is introduced and studied. The ratio test is used to determine the radius of convergence in which this matrix function is absolutely convergent. The domains in which the basic Gauss hypergeometric matrix function is invertible and its -derivative is bounded are determined. Hypergeometric matrix -difference equation is introduced and two solutions to this equation are found as terms of basic Gauss hypergeometric matrix function. The -integral representation for this matrix function is established.