Some inverse relations and theta function identities

Zhi Guo Liu

doi:10.1142/S1793042112501126

Some inverse relations and theta function identities

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Two pairs of inverse relations for elliptic theta functions are established with the method of Fourier series expansion, which allow us to recover many classical results in theta functions. Many nontrivial new theta function identities are discovered. Some curious trigonometric identities are derived.

Original language	English
Pages (from-to)	1977-2002
Number of pages	26
Journal	International Journal of Number Theory
Volume	8
Issue number	8
DOIs	https://doi.org/10.1142/S1793042112501126
State	Published - Dec 2012

Keywords

Elliptic function
Entire function
Fourier series
Schröter formula
Theta function

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10.1142/S1793042112501126

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title = "Some inverse relations and theta function identities",

abstract = "Two pairs of inverse relations for elliptic theta functions are established with the method of Fourier series expansion, which allow us to recover many classical results in theta functions. Many nontrivial new theta function identities are discovered. Some curious trigonometric identities are derived.",

keywords = "Elliptic function, Entire function, Fourier series, Schr{\"o}ter formula, Theta function",

author = "Liu, \{Zhi Guo\}",

year = "2012",

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doi = "10.1142/S1793042112501126",

language = "英语",

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T1 - Some inverse relations and theta function identities

AU - Liu, Zhi Guo

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AB - Two pairs of inverse relations for elliptic theta functions are established with the method of Fourier series expansion, which allow us to recover many classical results in theta functions. Many nontrivial new theta function identities are discovered. Some curious trigonometric identities are derived.

KW - Elliptic function

KW - Entire function

KW - Fourier series

KW - Schröter formula

KW - Theta function

UR - https://www.scopus.com/pages/publications/84866674460

U2 - 10.1142/S1793042112501126

DO - 10.1142/S1793042112501126

M3 - 文章

AN - SCOPUS:84866674460

SN - 1793-0421

VL - 8

SP - 1977

EP - 2002

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 8

ER -

Some inverse relations and theta function identities

Abstract

Keywords

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