Modular equations for the Rogers-Ramanujan continued fraction and the Dedekind eta-function

被引：10

作者：

Yi, JH ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

RAMANUJAN JOURNAL | 2001年 / 5卷 / 04期

关键词：

modular equation; Rogers-Ramanujan continued fraction; Dedekind eta-function;

D O I：

10.1023/A:1013991704758

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

S. Ramanujan recorded five beautiful identities providing relations between the Rogers-Ramanujan continued fraction R(q) and the five continued fractions R(-q), R(q(2)), R(q(3)), R(q(4)), and R(q(5)), summarized on page 365 of his Lost Notebook. We give new proofs for two of them by using new eta-function identities, and we also present a new relation between R(q) and R(q(7)).

引用

页码：377 / 384

页数：8

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