Fungrim entry: cb6c9c

\theta_{3}\!\left(0 , 5 i\right) = \left[\frac{\sqrt{5 + 2 \sqrt{5}}}{{5}^{3 / 4}}\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{\sqrt{5 + 2 \sqrt{5}}}{{5}^{3 / 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
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power

Source code for this entry:

Entry(ID("cb6c9c"),
    Formula(Equal(JacobiTheta(3, 0, Mul(5, ConstI)), Mul(Brackets(Div(Sqrt(Add(5, Mul(2, Sqrt(5)))), Pow(5, Div(3, 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