Fungrim entry: f12e20

\theta_{3}\!\left(0 , 3 i\right) = \left[\frac{\sqrt{\sqrt{3} + 1}}{{2}^{1 / 4} \cdot {3}^{3 / 8}}\right] \theta_{3}\!\left(0 , i\right)

References:

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

TeX:

\theta_{3}\!\left(0 , 3 i\right) = \left[\frac{\sqrt{\sqrt{3} + 1}}{{2}^{1 / 4} \cdot  {3}^{3 / 8}}\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("f12e20"),
    Formula(Equal(JacobiTheta(3, 0, Mul(3, ConstI)), Mul(Brackets(Div(Sqrt(Add(Sqrt(3), 1)), Mul(Pow(2, Div(1, 4)), Pow(3, Div(3, 8))))), 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