# Fungrim entry: 5384f3

$\theta_{3}\!\left(0 , 1 + 6 i\right) = \left[\frac{{\left(1 + \sqrt{3} + \sqrt{2} {\left(27\right)}^{1 / 4}\right)}^{1 / 3}}{{2}^{11 / 24} \cdot {3}^{3 / 8} {\left(\sqrt{3} - 1\right)}^{1 / 6}}\right] \theta_{3}\!\left(0 , i\right)$
References:
• https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 1 + 6 i\right) = \left[\frac{{\left(1 + \sqrt{3} + \sqrt{2} {\left(27\right)}^{1 / 4}\right)}^{1 / 3}}{{2}^{11 / 24} \cdot  {3}^{3 / 8} {\left(\sqrt{3} - 1\right)}^{1 / 6}}\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("5384f3"),
Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(6, ConstI))), Mul(Brackets(Div(Pow(Add(Add(1, Sqrt(3)), Mul(Sqrt(2), Pow(Parentheses(27), Div(1, 4)))), Div(1, 3)), Mul(Mul(Pow(2, Div(11, 24)), Pow(3, Div(3, 8))), Pow(Sub(Sqrt(3), 1), Div(1, 6))))), JacobiTheta(3, 0, ConstI)))),
References("https://doi.org/10.1016/j.jmaa.2003.12.009"))

## Topics using this entry

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