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Fungrim entry: 7e0002

θ3 ⁣(2z,2τ)=θ32 ⁣(z,τ)+θ42 ⁣(z,τ)2θ3 ⁣(0,2τ)\theta_{3}\!\left(2 z , 2 \tau\right) = \frac{\theta_{3}^{2}\!\left(z, \tau\right) + \theta_{4}^{2}\!\left(z, \tau\right)}{2 \theta_{3}\!\left(0 , 2 \tau\right)}
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\theta_{3}\!\left(2 z , 2 \tau\right) = \frac{\theta_{3}^{2}\!\left(z, \tau\right) + \theta_{4}^{2}\!\left(z, \tau\right)}{2 \theta_{3}\!\left(0 , 2 \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
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("7e0002"),
    Formula(Equal(JacobiTheta(3, Mul(2, z), Mul(2, tau)), Div(Add(Pow(JacobiTheta(3, z, tau), 2), Pow(JacobiTheta(4, z, tau), 2)), Mul(2, JacobiTheta(3, 0, Mul(2, 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.

2019-09-20 18:07:53.062439 UTC