Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi

被引：4

作者：

Berndt, Bruce C. ^{[1
]}

Lamb, George

Rogers, Mathew ^{[2
]}

机构：

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

[2] Univ Montreal, Dept Math & Stat, Montreal, PQ H3T 1J4, Canada

来源：

RAMANUJAN JOURNAL | 2012年 / 29卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

Two-dimensional lattice sums; Ramanujan's theta functions; Class invariants; Singular moduli; Rogers-Ramanujan continued fraction; Cubic continued fraction; Jacobian elliptic functions; Hypergeometric functions; LATTICE SUMS;

D O I：

10.1007/s11139-011-9351-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We evaluate in closed form, for the first time, certain classes of double series, which are remindful of lattice sums. Elliptic functions, singular moduli, class invariants, and the Rogers-Ramanujan continued fraction play central roles in our evaluations.

引用

页码：185 / 198

页数：14

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