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Fungrim entry: 52302f

θ3 ⁣(0,i3)=[(23+3)1/4]θ3 ⁣(0,i)\theta_{3}\!\left(0 , \frac{i}{3}\right) = \left[{\left(2 \sqrt{3} + 3\right)}^{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}{3}\right) = \left[{\left(2 \sqrt{3} + 3\right)}^{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
Powab{a}^{b} Power
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("52302f"),
    Formula(Equal(JacobiTheta(3, 0, Div(ConstI, 3)), Mul(Brackets(Pow(Add(Mul(2, Sqrt(3)), 3), Div(1, 4))), JacobiTheta(3, 0, ConstI)))),
    References("https://doi.org/10.1016/j.jmaa.2003.12.009"))

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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