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Fungrim entry: b58070

θ3 ⁣(0,1+2i)=[21/8]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 1 + 2 i\right) = \left[{2}^{-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 , 1 + 2 i\right) = \left[{2}^{-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
Powab{a}^{b} Power
Source code for this entry:
Entry(ID("b58070"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(2, ConstI))), Mul(Brackets(Pow(2, Neg(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.

2019-09-22 15:43:45.410764 UTC