青本广义超几何函数的要素及对高斯超几何微分方程的新视角
偏微分方程分析
2018-10-12 v1 高能物理 - 理论
数学物理
math.MP
摘要
我们回顾了 Grassmann 空间 Gr(k+1, n+1) 上的青本广义超几何函数。特别地，我们基于扭曲同调与上同调澄清了广义超几何函数的积分表示。以 Gr(2,4) 情形为例，我们在青本框架下详细考察了高斯原始超几何函数。这引导我们以一阶 Fuchs 型微分方程的形式给出高斯超几何微分方程的一种新的系统性描述。
引用
@article{arxiv.1810.04850,
title = {Elements of Aomoto's generalized hypergeometric functions and a novel perspective on Gauss' hypergeometric differential equation},
author = {Yasuhiro Abe},
journal= {arXiv preprint arXiv:1810.04850},
year = {2018}
}
备注
20 pages, invited chapter contribution to "Advances in Special Functions and Analysis of Differential Equations," CRC Press, (to be) edited by Praveen Agarwal, Ravi P Agarwal and Michael Ruzhansky. Contents are mainly based on some part of Nucl. Phys. B907:107-153, 2016 (arXiv:1512.06476 [hep-th]) by the author