Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind

Heng Huat Chan; Zhi Guo Liu

doi:10.1016/S0001-8708(02)00054-3

Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind

Heng Huat Chan
, Zhi Guo Liu^*

^*此作品的通讯作者

数学科学学院

University of Sussex
National University of Singapore

科研成果: 期刊稿件 › 文献综述 › 同行评审

10 引用（Scopus）

摘要

In this article, we revisit Ramanujan's cubic analogue of Jacobi's inversion formula for the classical elliptic integral of the first kind. Our work is motivated by the recent work of Milne (Ramanujan J. 6(1) (2002) 7-149), Chan and Chua (Ramanujan J., to appear) on the representations of integers as sums of even squares.

源语言	英语
页（从-至）	69-88
页数	20
期刊	Advances in Mathematics
卷	174
期	1
DOI	https://doi.org/10.1016/S0001-8708(02)00054-3
出版状态	已出版 - 1 3月 2003

访问文件

10.1016/S0001-8708(02)00054-3

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{0b29775dc833408ba84a793c5d4f454a,

title = "Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind",

abstract = "In this article, we revisit Ramanujan's cubic analogue of Jacobi's inversion formula for the classical elliptic integral of the first kind. Our work is motivated by the recent work of Milne (Ramanujan J. 6(1) (2002) 7-149), Chan and Chua (Ramanujan J., to appear) on the representations of integers as sums of even squares.",

keywords = "Cubic theta functions, Eisenstein series, Incomplete elliptic integrals",

author = "Chan, \{Heng Huat\} and Liu, \{Zhi Guo\}",

year = "2003",

month = mar,

day = "1",

doi = "10.1016/S0001-8708(02)00054-3",

language = "英语",

volume = "174",

pages = "69--88",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind

AU - Chan, Heng Huat

AU - Liu, Zhi Guo

PY - 2003/3/1

Y1 - 2003/3/1

N2 - In this article, we revisit Ramanujan's cubic analogue of Jacobi's inversion formula for the classical elliptic integral of the first kind. Our work is motivated by the recent work of Milne (Ramanujan J. 6(1) (2002) 7-149), Chan and Chua (Ramanujan J., to appear) on the representations of integers as sums of even squares.

AB - In this article, we revisit Ramanujan's cubic analogue of Jacobi's inversion formula for the classical elliptic integral of the first kind. Our work is motivated by the recent work of Milne (Ramanujan J. 6(1) (2002) 7-149), Chan and Chua (Ramanujan J., to appear) on the representations of integers as sums of even squares.

KW - Cubic theta functions

KW - Eisenstein series

KW - Incomplete elliptic integrals

UR - https://www.scopus.com/pages/publications/0037343490

U2 - 10.1016/S0001-8708(02)00054-3

DO - 10.1016/S0001-8708(02)00054-3

M3 - 文献综述

AN - SCOPUS:0037343490

SN - 0001-8708

VL - 174

SP - 69

EP - 88

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind

摘要

访问文件

其它文件与链接

学术指纹

引用此