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Fungrim entry: abc1e7

θ1 ⁣(z,τ+8n)=θ1 ⁣(z,τ)\theta_{1}\!\left(z , \tau + 8 n\right) = \theta_{1}\!\left(z , \tau\right)
Assumptions:z∈C  and⁡  τ∈H  and⁡  n∈Zz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
TeX:
\theta_{1}\!\left(z , \tau + 8 n\right) = \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
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("abc1e7"),
    Formula(Equal(JacobiTheta(1, z, Add(tau, Mul(8, 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