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arXiv · 1703.03036

On transformations of A-hypergeometric functions

Jens Forsgård·Laura Felicia Matusevich·Aleksandra Sobieska
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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.

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Jens Forsgård, Laura Felicia Matusevich, Aleksandra Sobieska. 2017-03-08. On transformations of A-hypergeometric functions. https://arxiv.org/abs/1703.03036

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