Fungrim entry: 390158

$\theta_{3}\!\left(0 , 1 + 10 i\right) = \left[\frac{{2}^{7 / 8}}{\left({5}^{1 / 4} - 1\right) \sqrt{5 \sqrt{5} + 5}}\right] \theta_{3}\!\left(0 , i\right)$
References:
• https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 1 + 10 i\right) = \left[\frac{{2}^{7 / 8}}{\left({5}^{1 / 4} - 1\right) \sqrt{5 \sqrt{5} + 5}}\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("390158"),
Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(10, ConstI))), Mul(Brackets(Div(Pow(2, Div(7, 8)), Mul(Sub(Pow(5, Div(1, 4)), 1), Sqrt(Add(Mul(5, Sqrt(5)), 5))))), 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