Sixteen Eisenstein series

被引：7
|
作者：
Cooper, Shaun [1 ]
Lam, Heung Yeung [1 ]
机构：
[1] Massey Univ, Inst Informat & Math Sci, N Shore Mail Ctr, Auckland, New Zealand
来源：
RAMANUJAN JOURNAL | 2009年 / 18卷 / 01期
关键词：
Eisenstein series; Elliptic function; Ramanujan's Notebooks; Theta function; SUMMATION;
D O I：
10.1007/s11139-007-9039-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
S. Ramanujan gave fourteen families of series in his Second Notebook in Chap. 17, Entries 13-17. In each case he gave only the first few examples, giving us the motivation to find and prove a general formula for each family of series. The aim of this paper is to develop a powerful tool (four versatile functions f (0),f (1),f (2), and f (3)) to collect all of Ramanujan's examples together.
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页码：33 / 59
页数：27
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