An elementary proof of Ramanujan's circular summation formula and its generalizations

被引：8
|
作者：
Xu, Ping [1 ]
机构：
[1] Univ Illinois, Urbana, IL 61801 USA
来源：
RAMANUJAN JOURNAL | 2012年 / 27卷 / 03期
关键词：
Ramanujan's circular summation; Generalizations; Elementary method; THETA-FUNCTIONS; LOST NOTEBOOK; POWERS;
D O I：
10.1007/s11139-011-9364-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we give a completely elementary proof of Ramanujan's circular summation formula of theta functions and its generalizations given by S.H. Chan and Z.-G. Liu, who used the theory of elliptic functions. In contrast to all other proofs, our proofs are elementary. An application of this summation formula is given.
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页码：409 / 417
页数：9
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