A bivariate circular summation formula for cubic theta functions and its implications

被引：0
|
作者：
Dai, Tianzhu [1 ]
Ma, Xinrong [1 ]
机构：
[1] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China
来源：
JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY | 2011年 / 26卷 / 03期
关键词：
FUNCTION IDENTITY;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a general bivariate circular summation formula and its dual form are established. They connect Ramanujan's theta function with the cubic analogue, Sigma(infinity)(m,n=-infinity) q(m2+mn+n2)x(m), of the classical theta functions introduced by M. Hirschhorn, F. Garvan and J. Borwein [18]. As applications, many new theta function identities are found and some well-known results are recovered from this summation formula as well as its dual form.
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收藏
页码：237 / 259
页数：23
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