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Fungrim entry: 47f6dd

θ2 ⁣(z+12,τ)=−θ1 ⁣(z,τ)\theta_{2}\!\left(z + \frac{1}{2} , \tau\right) = -\theta_{1}\!\left(z , \tau\right)
Assumptions:z∈C  and⁡  τ∈Hz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
TeX:
\theta_{2}\!\left(z + \frac{1}{2} , \tau\right) = -\theta_{1}\!\left(z , \tau\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
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
Source code for this entry:
Entry(ID("47f6dd"),
    Formula(Equal(JacobiTheta(2, Add(z, Div(1, 2)), tau), Neg(JacobiTheta(1, z, tau)))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

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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