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# Fungrim entry: b978f0

$\theta_{1}\!\left(z , \tau + 2 n\right) = {i}^{n} \theta_{1}\!\left(z , \tau\right)$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}$
TeX:
\theta_{1}\!\left(z , \tau + 2 n\right) = {i}^{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
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("b978f0"),
Formula(Equal(JacobiTheta(1, z, Add(tau, Mul(2, n))), Mul(Pow(ConstI, 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.

2020-01-31 18:09:28.494564 UTC