# Fungrim entry: 4cf228

$\theta_{2}\!\left(z , \tau + 4 n\right) = {\left(-1\right)}^{n} \theta_{2}\!\left(z , \tau\right)$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}$
TeX:
\theta_{2}\!\left(z , \tau + 4 n\right) = {\left(-1\right)}^{n} \theta_{2}\!\left(z , \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("4cf228"),
Formula(Equal(JacobiTheta(2, z, Add(tau, Mul(4, n))), Mul(Pow(-1, n), JacobiTheta(2, z, tau)))),
Variables(z, tau, n),
Assumptions(And(Element(z, CC), Element(tau, HH), Element(n, ZZ))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-01-31 18:09:28.494564 UTC