XXII.—Integration of a Certain System of Linear Partial Differential Equations of Hypergeometric Type

Abstract

1. The integration of systems of linear partial differential equations of hypergeometric type has been the subject of a great number of recent investigations (e.g. Appell, 1925; Appell-Kampé de Fériet, 1926). Especially Professor Horn (see references) and his pupils, for instance Borngässer (1933), have done much valuable work in this field.The first method that suggests itself for integrating systems of this type is to try power-series expansions of the solutions in the neighbourhood of the singular points of the system. This method, however, does not yield in general a complete set of solutions. Those singular points of the system in which more than n singular manifolds intersect, n being the number of independent variables, give rise to considerable difficulties.