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Fungrim entry: f12e20

θ3 ⁣(0,3i)=[3+121/433/8]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 3 i\right) = \left[\frac{\sqrt{\sqrt{3} + 1}}{{2}^{1 / 4} {3}^{3 / 8}}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 3 i\right) = \left[\frac{\sqrt{\sqrt{3} + 1}}{{2}^{1 / 4} {3}^{3 / 8}}\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("f12e20"),
    Formula(Equal(JacobiTheta(3, 0, Mul(3, ConstI)), Mul(Brackets(Div(Sqrt(Add(Sqrt(3), 1)), Mul(Pow(2, Div(1, 4)), Pow(3, Div(3, 8))))), 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