Contiguity relations of Lauricella's F_D revisited

TL;DR

This paper revisits the contiguity relations of Lauricella's hypergeometric function F_D using twisted cohomology and intersection forms, deriving new relations and constructing solutions as Laurent series.

Contribution

It introduces a cohomological approach to derive contiguity relations and constructs explicit solutions for F_D, enhancing understanding of its differential system.

Findings

Derived new contiguity relations using twisted cohomology

Expressed solutions as Laurent series with explicit coefficients

Constructed twisted cycles corresponding to fundamental solutions

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.