On transformations of A-hypergeometric functions

2017/03/08 by Jens Forsgård, Forsgård, Jens, Laura Felicia Matusevich +3
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AG #math.CA #math.CV #msc:14M25 #msc:32A17 #msc:33C70

paper · pdf · doi:10.48550/arxiv.1703.03036

arxiv created 2017/03/08 · arxiv updated 2017/03/10

Abstract

We propose a systematic study of transformations of A-hypergeometric functions. Our approach is to apply changes of variables corresponding to automorphisms of toric rings, to Euler-type integral representations of A-hypergeometric functions. We show that all linear A-hypergeometric transformations arise from symmetries of the corresponding polytope. As an application of the techniques developed here, we show that the Appell function F₄ does not admit a certain kind of Euler-type integral representation.

Citations

• Euler--Mellin integrals and A-hypergeometric functions

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