Contiguity relations of Aomoto-Gel'fand hypergeometric functions and applications to Appell's system f 3 and Goursta's systems 3 F 2
Contiguity relations of Aomoto-Gel'fand hypergeometric functions and applications to Appell's system f 3 and Goursta's systems 3 F 2
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Aomoto-Gelfand 超几何函数的邻接关系及其在 Appell 系统 f 3 和 Goursta 系统 3 F 2 中的应用
DOI：
10.1137/0522052
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发表时间：
1991
影响因子：
2
通讯作者：
Takeshi Sasaki
中科院分区：
文献类型：
--
作者：
Takeshi Sasaki
Aomoto-Gel’fand 超几何函数 $\Phi (Z,\alpha )$ [K.青本，科学。论文，东京大学文理学院，27 (1977)，第 49–61 页]，[I. M. Gel'fand，苏联数学。 Dokl., 33 (1986), pp. 573–577] 是在格拉斯曼 $G_{k,n} $（n 维线性空间的 k 维子空间集）上定义的 z 函数，并具有复数参数 $(\alpha )$。这类函数包含某些经典的超几何函数（HGF），例如高斯的HGF、广义的HGF ${}_{p + 1} F_p $，以及Appell的HGF的$F_1 $、$F_2 $、$F_3 $。另一方面，W. Miller [J.数学。物理学，13 (1972)，第 1393–1399 页；暹罗 J. 应用程序。 《数学》，25 (1973)，第 226–235 页；暹罗 J. 数学。 Anal., 3 (1972), pp. 31–44] 给出了几个 HGF 的邻接关系，包括上面提到的 HGF，并显示了这些函数满足的方程的李代数结构。本文首先提出了获取 Aomoto-Gel’fand HGF 和 cl 的邻接关系的原理...
Aomoto–Gel’fand hypergeometric functions $\Phi (Z,\alpha )$ [K. Aomoto, Sci. Papers, College of Arts and Sciences, University of Tokyo, 27 (1977), pp. 49–61], [I. M. Gel’fand, Soviet Math. Dokl., 33 (1986), pp. 573–577] are functions of z defined on the Grassmannian $G_{k,n} $, the set of k-dimensional subspaces of an n-dimensional linear space, and with complex parameters $(\alpha )$. Such a class of functions contains certain classical hypergeometric functions (HGF), such as the HGF of Gauss, the generalized HGF ${}_{p + 1} F_p $, and Appell’s HGF’s $F_1 $, $F_2 $, $F_3 $. On the other hand, W. Miller [J. Math. Phys.,13 (1972), pp. 1393–1399; SIAM J. Appl. Math., 25 (1973), pp. 226–235; SIAM J. Math. Anal., 3 (1972), pp. 31–44] has given contiguity relations for several HGF’s, including the HGF’s mentioned above, and has shown the Lie-algebraic structure of the equations satisfied by these functions. This paper first presents a principle of obtaining contiguity relations for Aomoto–Gel’fand HGF’s and cl...