On a fundamental system of solutions of a certain hypergeometric equation

Abstract

We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gauß's ${}_2{F}_1$, Thomae's ${}_L{F}_{L-1}$ and Appell-Lauricella's $F_D$. In particular, we present a fundamental system of solutions with a characteristic local behavior by means of Euler-type integral representations. We also discuss how they are related to the theory of isomonodromic deformations or Painlevé equations.

19 pages