Fungrim home page

Fungrim entry: 4256f0

θ3 ⁣(0,i2)=[2+1221/4]θ3 ⁣(0,i)\theta_{3}\!\left(0 , \frac{i}{2}\right) = \left[\sqrt{\frac{\sqrt{2} + 1}{2}} {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}} {2}^{1 / 4}\right] \theta_{3}\!\left(0 , i\right)
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
Powab{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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-20 18:07:53.062439 UTC