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Fungrim entry: 8356db

θ3 ⁣(0,9i)=[1+(2(3+1))1/33]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 9 i\right) = \left[\frac{1 + {\left(2 \left(\sqrt{3} + 1\right)\right)}^{1 / 3}}{3}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 9 i\right) = \left[\frac{1 + {\left(2 \left(\sqrt{3} + 1\right)\right)}^{1 / 3}}{3}\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("8356db"),
    Formula(Equal(JacobiTheta(3, 0, Mul(9, ConstI)), Mul(Brackets(Div(Add(1, Pow(Mul(2, Add(Sqrt(3), 1)), Div(1, 3))), 3)), 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.

2019-09-22 15:43:45.410764 UTC