Fungrim entry: 95e9e4

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

References:

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

TeX:

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

Source code for this entry:

Entry(ID("95e9e4"),
    Formula(Equal(JacobiTheta(3, 0, Mul(4, ConstI)), Mul(Brackets(Div(Add(1, Pow(2, Neg(Div(1, 4)))), 2)), 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