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Contiguity relations of Lauricella’s $$F_D$$ revisited. (English) Zbl 1371.33027
Summary: 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.

MSC:
 33C65 Appell, Horn and Lauricella functions 33C90 Applications of hypergeometric functions
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