Fungrim entry: 53fef4

\theta_{3}\!\left(2 z , 4 \tau\right) = \frac{\theta_{3}\!\left(z , \tau\right) + \theta_{4}\!\left(z , \tau\right)}{2}

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}

TeX:

\theta_{3}\!\left(2 z , 4 \tau\right) = \frac{\theta_{3}\!\left(z , \tau\right) + \theta_{4}\!\left(z , \tau\right)}{2}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}

Definitions:

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

Source code for this entry:

Entry(ID("53fef4"),
    Formula(Equal(JacobiTheta(3, Mul(2, z), Mul(4, tau)), Div(Add(JacobiTheta(3, z, tau), JacobiTheta(4, z, 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.

2021-03-15 19:12:00.328586 UTC