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Fungrim entry: 324483

θ3 ⁣(0,1+i2)=[(21)2/3(4+32)1/1227/24]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 1 + \frac{i}{2}\right) = \left[\frac{{\left(\sqrt{2} - 1\right)}^{2 / 3} {\left(4 + 3 \sqrt{2}\right)}^{1 / 12}}{{2}^{7 / 24}}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 1 + \frac{i}{2}\right) = \left[\frac{{\left(\sqrt{2} - 1\right)}^{2 / 3} {\left(4 + 3 \sqrt{2}\right)}^{1 / 12}}{{2}^{7 / 24}}\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("324483"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, Div(ConstI, 2))), Mul(Brackets(Div(Mul(Pow(Sub(Sqrt(2), 1), Div(2, 3)), Pow(Add(4, Mul(3, Sqrt(2))), Div(1, 12))), Pow(2, Div(7, 24)))), 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