On an identity of Ramanujan based on the hypergeometric series 2F1(1/3,2/3; 1/2; x).

被引：14

作者：

Shen, LC ^{[1
]}

机构：

[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA

来源：

JOURNAL OF NUMBER THEORY | 1998年 / 69卷 / 02期

关键词：

D O I：

10.1006/jnth.1997.2212

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently, B. C. Berndt, S. Bhargava and F. Garvan provided the first proof to an identity of Ramanujan. Their proof, which is based on various modular identities, is quite difficult and complicated. In this paper, we give a much simpler proof of this identity by converting it into an identity involving the classical elliptic functions and establishing the identity by comparing their Laurent series expansions at a pole. (C) 1998 Academic Press.

引用

页码：125 / 134

页数：10