# Fungrim entry: 669765

$\theta_{3}\!\left(0 , 6 i\right) = \left[\frac{{\left(-4 + 3 \sqrt{2} + {3}^{5 / 4} + 2 \sqrt{3} - {3}^{3 / 4} + 2 \sqrt{2} \left({3}^{3 / 4}\right)\right)}^{1 / 3}}{2 \left({3}^{3 / 8}\right) {\left(\left(\sqrt{2} - 1\right) \left(\sqrt{3} - 1\right)\right)}^{1 / 6}}\right] \theta_{3}\!\left(0 , i\right)$
References:
• https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 6 i\right) = \left[\frac{{\left(-4 + 3 \sqrt{2} + {3}^{5 / 4} + 2 \sqrt{3} - {3}^{3 / 4} + 2 \sqrt{2} \left({3}^{3 / 4}\right)\right)}^{1 / 3}}{2 \left({3}^{3 / 8}\right) {\left(\left(\sqrt{2} - 1\right) \left(\sqrt{3} - 1\right)\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("669765"),
Formula(Equal(JacobiTheta(3, 0, Mul(6, ConstI)), Mul(Brackets(Div(Pow(Add(Sub(Add(Add(Add(-4, Mul(3, Sqrt(2))), Pow(3, Div(5, 4))), Mul(2, Sqrt(3))), Pow(3, Div(3, 4))), Mul(Mul(2, Sqrt(2)), Parentheses(Pow(3, Div(3, 4))))), Div(1, 3)), Mul(Mul(2, Parentheses(Pow(3, Div(3, 8)))), Pow(Mul(Sub(Sqrt(2), 1), 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.

2020-01-31 18:09:28.494564 UTC