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Fungrim entry: 5384f3

θ3 ⁣(0,1+6i)=[(1+3+2(27)1/4)1/3211/2433/8(31)1/6]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 1 + 6 i\right) = \left[\frac{{\left(1 + \sqrt{3} + \sqrt{2} {\left(27\right)}^{1 / 4}\right)}^{1 / 3}}{{2}^{11 / 24} {3}^{3 / 8} {\left(\sqrt{3} - 1\right)}^{1 / 6}}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 1 + 6 i\right) = \left[\frac{{\left(1 + \sqrt{3} + \sqrt{2} {\left(27\right)}^{1 / 4}\right)}^{1 / 3}}{{2}^{11 / 24} {3}^{3 / 8} {\left(\sqrt{3} - 1\right)}^{1 / 6}}\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("5384f3"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(6, ConstI))), Mul(Brackets(Div(Pow(Add(Add(1, Sqrt(3)), Mul(Sqrt(2), Pow(Parentheses(27), Div(1, 4)))), Div(1, 3)), Mul(Mul(Pow(2, Div(11, 24)), Pow(3, Div(3, 8))), Pow(Sub(Sqrt(3), 1), Div(1, 6))))), JacobiTheta(3, 0, ConstI)))),
    References("https://doi.org/10.1016/j.jmaa.2003.12.009"))

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2019-09-20 18:07:53.062439 UTC