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Fungrim entry: 390158

θ3 ⁣(0,1+10i)=[27/8(51/4−1)55+5]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 1 + 10 i\right) = \left[\frac{{2}^{7 / 8}}{\left({5}^{1 / 4} - 1\right) \sqrt{5 \sqrt{5} + 5}}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 1 + 10 i\right) = \left[\frac{{2}^{7 / 8}}{\left({5}^{1 / 4} - 1\right) \sqrt{5 \sqrt{5} + 5}}\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("390158"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(10, ConstI))), Mul(Brackets(Div(Pow(2, Div(7, 8)), Mul(Sub(Pow(5, Div(1, 4)), 1), Sqrt(Add(Mul(5, Sqrt(5)), 5))))), JacobiTheta(3, 0, ConstI)))),
    References("https://doi.org/10.1016/j.jmaa.2003.12.009"))

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2021-03-15 19:12:00.328586 UTC