Fungrim entry: 483e7e

\theta_{3}\!\left(0 , 5 i\right) = \left[\frac{1}{\sqrt{5 \sqrt{5} - 10}}\right] \theta_{3}\!\left(0 , i\right)

References:

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

TeX:

\theta_{3}\!\left(0 , 5 i\right) = \left[\frac{1}{\sqrt{5 \sqrt{5} - 10}}\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
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("483e7e"),
    Formula(Equal(JacobiTheta(3, 0, Mul(5, ConstI)), Mul(Brackets(Div(1, Sqrt(Sub(Mul(5, Sqrt(5)), 10)))), 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