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Fungrim entry: 7527f1

θ42 ⁣(0,τ2)=θ32 ⁣(0,τ)θ22 ⁣(0,τ)\theta_{4}^{2}\!\left(0, \frac{\tau}{2}\right) = \theta_{3}^{2}\!\left(0, \tau\right) - \theta_{2}^{2}\!\left(0, \tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta_{4}^{2}\!\left(0, \frac{\tau}{2}\right) = \theta_{3}^{2}\!\left(0, \tau\right) - \theta_{2}^{2}\!\left(0, \tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("7527f1"),
    Formula(Equal(Pow(JacobiTheta(4, 0, Div(tau, 2)), 2), Sub(Pow(JacobiTheta(3, 0, tau), 2), Pow(JacobiTheta(2, 0, tau), 2)))),
    Variables(tau),
    Assumptions(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.

2019-09-22 15:43:45.410764 UTC