Tohoku Mathematical Journal
2017
June
SECOND SERIES VOL. 69, NO. 2

Tohoku Math. J.
69 (2017), 287-304

Title CONTIGUITY RELATIONS OF LAURICELLA'S $F_D$ REVISITED

Author Yoshiaki Goto

(Received January 23, 2015, revised August 12, 2015)
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.

Mathematics Subject Classification. Primary 33C65; Secondary 33C90.
Key words and phrases. Lauricella's $F_D$, contiguity relations, twisted (co)homology groups, contingency tables.

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