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

TL;DR

This paper investigates Pfaffian equations and contiguity relations of a specific hypergeometric function using twisted cohomology, and applies these findings to compute normalizing constants in algebraic statistics.

Contribution

It introduces a novel approach using twisted cohomology to analyze hypergeometric functions and applies it to a practical problem in algebraic statistics.

Findings

Derived Pfaffian equations and contiguity relations for the hypergeometric function.

Applied the theoretical results to evaluate normalizing constants in contingency tables.

Enhanced computational methods in algebraic statistics.

Abstract

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