On Transformations of <i>A</i>-Hypergeometric Functions

DOI10.1619/FESI.62.319zbMATH Open1440.33014arXiv1703.03036OpenAlexW3008453223MaRDI QIDQ5110296

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Publication date: 18 May 2020

Published in: (Search for Journal in Brave)

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 $F_4$ does not admit a certain kind of Euler-type integral representation.

Full work available at URL: https://arxiv.org/abs/1703.03036

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