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Fungrim entry: e56f77

θ3 ⁣(z+2n,τ)=θ3 ⁣(z,τ)\theta_{3}\!\left(z + 2 n , \tau\right) = \theta_{3}\!\left(z , \tau\right)
Assumptions:zCandτHandnZz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\theta_{3}\!\left(z + 2 n , \tau\right) = \theta_{3}\!\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
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("e56f77"),
    Formula(Equal(JacobiTheta(3, Add(z, Mul(2, n)), tau), JacobiTheta(3, 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.

2019-08-19 14:38:23.809000 UTC