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.

引用

页码：409 / 417

页数：9

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