关于A-超几何函数的变换

IF 0.7 4区数学 Q2 MATHEMATICS

Funkcialaj Ekvacioj-Serio Internacia Pub Date : 2017-03-08 DOI:10.1619/fesi.62.319

J. Forsgaard, L. Matusevich, Aleksandra Sobieska

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引用次数: 1

摘要

我们提出了一个系统的研究$a$-超几何函数的变换。我们的方法是将对应于复曲面环的自同构的变量的变化应用于$A$-超几何函数的欧拉型积分表示。我们证明了所有线性$A$-超几何变换都是由对应多面体的对称性引起的。作为本文技术的一个应用，我们证明了Appel函数$F_4$不允许某一类欧拉型积分表示。

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On Transformations of A-Hypergeometric Functions

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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