THE COMMON LIMIT OF A QUADRUPLE SEQUENCE AND THE HYPERGEOMETRIC FUNCTION FD OF THREE VARIABLES

被引：4

作者：

Kato, Takayuki ^{[1
]}

Matsumoto, Keiji ^{[2
]}

机构：

[1] MEC INC, Aoba Ku, Sendai, Miyagi 9800802, Japan

[2] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

来源：

NAGOYA MATHEMATICAL JOURNAL | 2009年 / 195卷

关键词：

AGM;

D O I：

10.1017/S0027763000009739

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a quadruple sequence and express its common limit by Lauricella's hypergeometric function F-D (1/4, 1/4, 1/4, 1/4, 1; z(1,) z(2,) z(3)) of three variables. We give a functional equation of F-D, which is the key to get our expression of the common limit.

引用

页码：113 / 124

页数：12

共 8 条

[1]

Borchardt C. W., 1876, BERL MONATSBER, V53, P611

[2] A CUBIC COUNTERPART OF JACOBIS IDENTITY AND THE AGM [J].