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Fungrim entry: 72f583

θ3 ⁣(0,7i)=[13+7+7+3714(28)1/8]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 7 i\right) = \left[\sqrt{\frac{\sqrt{13 + \sqrt{7}} + \sqrt{7 + 3 \sqrt{7}}}{14} {\left(28\right)}^{1 / 8}}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 7 i\right) = \left[\sqrt{\frac{\sqrt{13 + \sqrt{7}} + \sqrt{7 + 3 \sqrt{7}}}{14} {\left(28\right)}^{1 / 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("72f583"),
    Formula(Equal(JacobiTheta(3, 0, Mul(7, ConstI)), Mul(Brackets(Sqrt(Mul(Div(Add(Sqrt(Add(13, Sqrt(7))), Sqrt(Add(7, Mul(3, Sqrt(7))))), 14), Pow(Parentheses(28), Div(1, 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.

2019-09-20 18:07:53.062439 UTC