# Fungrim entry: 1fa8e7

$\theta_{1}\!\left(z , \tau + n\right) = {e}^{\pi i n / 4} \theta_{1}\!\left(z , \tau\right)$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}$
TeX:
\theta_{1}\!\left(z , \tau + n\right) = {e}^{\pi i n / 4} \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
Exp${e}^{z}$ Exponential function
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("1fa8e7"),
Formula(Equal(JacobiTheta(1, z, Add(tau, n)), Mul(Exp(Div(Mul(Mul(Pi, ConstI), n), 4)), 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.

2020-01-31 18:09:28.494564 UTC