A General Theta Function Identity and Modular Equations

XUE Lin, ZHANG Zhi-zheng

doi:10.13371/j.cnki.chin.q.j.m.2015.02.008

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 2: 211 - 217

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.02.008

A General Theta Function Identity and Modular Equations

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College of Mathematics, Luoyang Normal University

XUE Lin(1979-),female, native of Luoyang, Henan,an associate professor of Luoyang Normal University, M.S.D., engages in special functions; ZHANG Zhi-zheng(1964-), male, native of Jiaozuo, Henan, who has been out of two postdoctoral stations, a professor of Luoyang Normal University, engages in q-series and combinatorics and special functions.

Received date: 2014-11-03

Online published: 2020-11-23

Supported by

Supported by the National Natural Science Foundation of China(11071107,11371184)；

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Abstract

In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.

Key words： theta function; jacobian elliptic function; modular equations; quasi periods; pole

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XUE Lin, ZHANG Zhi-zheng . A General Theta Function Identity and Modular Equations[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(2) : 211 -217 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.02.008

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