FUCHSIAN INITIAL VALUE PROBLEM ON THE COMPLEX PROJECTIVE PLANE WITH HYPERGEOMETRIC FUNCTIONS AS DATA ALONG A LINE

Abstract

We consider a class of characteristic initial value problems on the complex projective plane. We give as initial functions on a line the Gauss hypergeometric function, and investigate what kind of solutions are obtained.We make use of the theory of the classical Euler-Poisson-Darboux equation to get an integral representation of the solution. The family of solutions contains Appell’s two-dimensional hypergeometric functions F₁ and F₂.