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.