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Fungrim entry: 6cbce8

θ3 ⁣(0,1+4i)=[2−7/16(2+1)1/4]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 1 + 4 i\right) = \left[{2}^{-7 / 16} {\left(\sqrt{2} + 1\right)}^{1 / 4}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 1 + 4 i\right) = \left[{2}^{-7 / 16} {\left(\sqrt{2} + 1\right)}^{1 / 4}\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("6cbce8"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(4, ConstI))), Mul(Brackets(Mul(Pow(2, Neg(Div(7, 16))), Pow(Add(Sqrt(2), 1), Div(1, 4)))), 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