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arXiv · 1904.00565

Euler and Laplace integral representations of GKZ hypergeometric functions

Saiei-Jaeyeong Matsubara-Heo
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Abstract

We introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We establish a combinatorial method of constructing a basis of the rapid decay homology group associated to Euler-Laplace integral with a nice intersection property. This construction yields a remarkable expansion formula of cohomology intersection numbers in terms of GKZ hypergeometric series. As an application, we obtain closed formulas of the quadratic relations of Aomoto-Gelfand hypergeometric functions and their confluent analogue in terms of bipartite graphs.

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Saiei-Jaeyeong Matsubara-Heo. 2019-04-01. Euler and Laplace integral representations of GKZ hypergeometric functions. https://arxiv.org/abs/1904.00565

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