Fungrim entry: 4256f0

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

References:

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

TeX:

\theta_{3}\!\left(0 , \frac{i}{2}\right) = \left[\sqrt{\frac{\sqrt{2} + 1}{2}} \cdot  {2}^{1 / 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("4256f0"),
    Formula(Equal(JacobiTheta(3, 0, Div(ConstI, 2)), Mul(Brackets(Mul(Sqrt(Div(Add(Sqrt(2), 1), 2)), Pow(2, Div(1, 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