Hypergeometric symbolic calculus. I: Systems of two symbolic hypergeometric equations (Q1865022)

The authors obtain the bases of solutions for all the 14 hypergeometric systems of Appel-Kampe de Feriet and Horn as well as integral representations for otherwise known solutions. They show that, in general, the space of solutions of a system consists of one analytic function in a neighborhood of the origin, and the other solutions are for most of the systems essentially a monomial \(x^\alpha y^\beta\) factor multiplied by an analytic function in a neighborhood of the origin. For certain systems there are special solutions which are convergent series in a cone \(|y / x |< \varepsilon\).