Fungrim home page

Fungrim entry: a9cdda

θ2 ⁣(z,τ2)=2θ2 ⁣(z,τ)θ3 ⁣(z,τ)θ2 ⁣(0,τ2)\theta_{2}\!\left(z , \frac{\tau}{2}\right) = \frac{2 \theta_{2}\!\left(z , \tau\right) \theta_{3}\!\left(z , \tau\right)}{\theta_{2}\!\left(0 , \frac{\tau}{2}\right)}
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\theta_{2}\!\left(z , \frac{\tau}{2}\right) = \frac{2 \theta_{2}\!\left(z , \tau\right) \theta_{3}\!\left(z , \tau\right)}{\theta_{2}\!\left(0 , \frac{\tau}{2}\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("a9cdda"),
    Formula(Equal(JacobiTheta(2, z, Div(tau, 2)), Div(Mul(Mul(2, JacobiTheta(2, z, tau)), JacobiTheta(3, z, tau)), JacobiTheta(2, 0, Div(tau, 2))))),
    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.

2019-10-05 13:11:19.856591 UTC