A CUBIC COUNTERPART OF JACOBIS IDENTITY AND THE AGM

被引：176

作者：

BORWEIN, JM

BORWEIN, PB

机构：

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1991年 / 323卷 / 02期

关键词：

MEAN ITERATIONS; THETA FUNCTIONS; HYPERGEOMETRIC FUNCTIONS; GENERALIZED ELLIPTIC FUNCTIONS; CUBIC TRANSFORMATIONS; PI; RAMANUJAN;

D O I：

10.2307/2001551

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We produce exact cubic analogues of Jacobi's celebrated theta function identity and of the arithmetic-geometric mean iteration of Gauss and Legendre. The interation in question is a(n+1): = 3/a(n) + 2b(n) and b(n+1): = 3 square-root b(n) (3/a(n)2 + a(n)b(n) + b(n)2). The limit of this iteration is identified in terms of the hypergeometric function 2F1(1/3, 2/3; 1; .), which supports a particularly simple cubic transformation.

引用

页码：691 / 701

页数：11