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Fungrim entry: e2bc80

θ3 ⁣(0,1+8i)=[27/8(16+1521/4+122+981/4)1/8]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 1 + 8 i\right) = \left[{2}^{-7 / 8} {\left(16 + 15 {2}^{1 / 4} + 12 \sqrt{2} + 9 {8}^{1 / 4}\right)}^{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 + 8 i\right) = \left[{2}^{-7 / 8} {\left(16 + 15 {2}^{1 / 4} + 12 \sqrt{2} + 9 {8}^{1 / 4}\right)}^{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
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("e2bc80"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(8, ConstI))), Mul(Brackets(Mul(Pow(2, Neg(Div(7, 8))), Pow(Add(Add(Add(16, Mul(15, Pow(2, Div(1, 4)))), Mul(12, Sqrt(2))), Mul(9, Pow(8, Div(1, 4)))), 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.

2019-09-20 18:07:53.062439 UTC