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^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Sussex
National University of Singapore

Research output: Contribution to journal › Review article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	69-88
Number of pages	20
Journal	Advances in Mathematics
Volume	174
Issue number	1
DOIs	https://doi.org/10.1016/S0001-8708(02)00054-3
State	Published - 1 Mar 2003

Keywords

Cubic theta functions
Eisenstein series
Incomplete elliptic integrals

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10.1016/S0001-8708(02)00054-3

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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.",

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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

Abstract

Keywords

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