Contiguity relations of Lauricella's $F_D$ revisited

Abstract

We study contiguity relations of Lauricella's hypergeometric function $F_D$, by using the twisted cohomology group and the intersection form. We derive contiguity relations from those in the twisted cohomology group and give the coefficients in these relations by the intersection numbers. Furthermore, we construct twisted cycles corresponding to a fundamental set of solutions to the system of differential equations satisfied by $F_D$, which are expressed as Laurent series. We also give the contiguity relations of these solutions.