Fungrim home page

Fungrim entry: 7137a2

θ2 ⁣(2z,2τ)=θ22 ⁣(z,τ)θ12 ⁣(z,τ)2θ3 ⁣(0,2τ)\theta_{2}\!\left(2 z , 2 \tau\right) = \frac{\theta_{2}^{2}\!\left(z, \tau\right) - \theta_{1}^{2}\!\left(z, \tau\right)}{2 \theta_{3}\!\left(0 , 2 \tau\right)}
Assumptions:zC  and  τHz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
\theta_{2}\!\left(2 z , 2 \tau\right) = \frac{\theta_{2}^{2}\!\left(z, \tau\right) - \theta_{1}^{2}\!\left(z, \tau\right)}{2 \theta_{3}\!\left(0 , 2 \tau\right)}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
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:
    Formula(Equal(JacobiTheta(2, Mul(2, z), Mul(2, tau)), Div(Sub(Pow(JacobiTheta(2, z, tau), 2), Pow(JacobiTheta(1, z, tau), 2)), Mul(2, JacobiTheta(3, 0, Mul(2, tau)))))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH))))

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