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Fungrim entry: 4c8873

θ3 ⁣(0,1+i)=[21/4]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 1 + i\right) = \left[{2}^{-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 + i\right) = \left[{2}^{-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
Source code for this entry:
Entry(ID("4c8873"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, ConstI)), Mul(Brackets(Pow(2, Neg(Div(1, 4)))), 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