Fungrim entry: 59184e

\theta'_{1}\!\left(0 , \frac{\tau}{2}\right) \theta_{2}\!\left(0 , \frac{\tau}{2}\right) = 2 \theta'_{1}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)

Assumptions:

\tau \in \mathbb{H}

TeX:

\theta'_{1}\!\left(0 , \frac{\tau}{2}\right) \theta_{2}\!\left(0 , \frac{\tau}{2}\right) = 2 \theta'_{1}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("59184e"),
    Formula(Equal(Mul(JacobiTheta(1, 0, Div(tau, 2), 1), JacobiTheta(2, 0, Div(tau, 2))), Mul(Mul(2, JacobiTheta(1, 0, tau, 1)), JacobiTheta(4, 0, tau)))),
    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.

2021-03-15 19:12:00.328586 UTC