Euler and Laplace integral representations of GKZ hypergeometric\n functions

2019/04/01 by Saiei-Jaeyeong Matsubara-Heo, Matsubara-Heo, Saiei-Jaeyeong · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1904.00565

openalex publication_date 2019/04/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We introduce an interpolation between Euler integral and Laplace integral:\nEuler-Laplace integral. We establish a combinatorial method of constructing a\nbasis of the rapid decay homology group associated to Euler-Laplace integral\nwith a nice intersection property. This construction yields a remarkable\nexpansion formula of cohomology intersection numbers in terms of GKZ\nhypergeometric series. As an application, we obtain closed formulas of the\nquadratic relations of Aomoto-Gelfand hypergeometric functions and their\nconfluent analogue in terms of bipartite graphs.\n

Citations

• Equivariant D-modules
• The Determinant of a Hypergeometric Period Matrix

Cited by

• Hypergeometric Discriminants

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