Fungrim entry: 8356db

\theta_{3}\!\left(0 , 9 i\right) = \left[\frac{1 + {\left(2 \left(\sqrt{3} + 1\right)\right)}^{1 / 3}}{3}\right] \theta_{3}\!\left(0 , i\right)

References:

https://doi.org/10.1016/j.jmaa.2003.12.009

TeX:

\theta_{3}\!\left(0 , 9 i\right) = \left[\frac{1 + {\left(2 \left(\sqrt{3} + 1\right)\right)}^{1 / 3}}{3}\right] \theta_{3}\!\left(0 , i\right)

Definitions:

Fungrim symbol	Notation	Short description
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`ConstI`	$i$	Imaginary unit
`Pow`	${a}^{b}$	Power
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("8356db"),
    Formula(Equal(JacobiTheta(3, 0, Mul(9, ConstI)), Mul(Brackets(Div(Add(1, Pow(Mul(2, Add(Sqrt(3), 1)), Div(1, 3))), 3)), JacobiTheta(3, 0, ConstI)))),
    References("https://doi.org/10.1016/j.jmaa.2003.12.009"))

Topics using this entry

Specific values of Jacobi theta functions

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