# Fungrim entry: 5cdae6

$\theta_{1}\!\left(z + n , \tau\right) = {\left(-1\right)}^{n} \theta_{1}\!\left(z , \tau\right)$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}$
TeX:
\theta_{1}\!\left(z + n , \tau\right) = {\left(-1\right)}^{n} \theta_{1}\!\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("5cdae6"),
Formula(Equal(JacobiTheta(1, Add(z, n), tau), Mul(Pow(-1, n), JacobiTheta(1, 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.

2021-03-15 19:12:00.328586 UTC