On a fundamental system of solutions of a certain hypergeometric equation

Teruhisa Tsuda

Published 2014-07-30, updated 2014-08-02Version 2

We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gau\ss'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 Painlev\'e equations.