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We study the structures of Pfaffian equations and contiguity relations of thehypergeometric function of type $(k+1,k+n+2)$ by using twisted cohomologygroups and the intersection form on them. We apply our results to algebraicstatistics; numerical evaluation of the normalizing constants of two waycontingency tables with fixed marginal sums.

Pfaffian equations and contiguity relations of the hypergeometric function of type $(k+1, k+n+2)$ and their applications