Fungrim entry: 52302f

\theta_{3}\!\left(0 , \frac{i}{3}\right) = \left[{\left(2 \sqrt{3} + 3\right)}^{1 / 4}\right] \theta_{3}\!\left(0 , i\right)

References:

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

TeX:

\theta_{3}\!\left(0 , \frac{i}{3}\right) = \left[{\left(2 \sqrt{3} + 3\right)}^{1 / 4}\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("52302f"),
    Formula(Equal(JacobiTheta(3, 0, Div(ConstI, 3)), Mul(Brackets(Pow(Add(Mul(2, Sqrt(3)), 3), Div(1, 4))), 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