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Fungrim entry: 7f9273

θ3 ⁣(0,i4)=[1+21/41+22+1221/2]θ3 ⁣(0,i)\theta_{3}\!\left(0 , \frac{i}{4}\right) = \left[\frac{1 + {2}^{-1 / 4}}{\sqrt{1 + \sqrt{2}}} \sqrt{\frac{\sqrt{2} + 1}{2}} {2}^{1 / 2}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , \frac{i}{4}\right) = \left[\frac{1 + {2}^{-1 / 4}}{\sqrt{1 + \sqrt{2}}} \sqrt{\frac{\sqrt{2} + 1}{2}} {2}^{1 / 2}\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("7f9273"),
    Formula(Equal(JacobiTheta(3, 0, Div(ConstI, 4)), Mul(Brackets(Mul(Mul(Div(Add(1, Pow(2, Neg(Div(1, 4)))), Sqrt(Add(1, Sqrt(2)))), Sqrt(Div(Add(Sqrt(2), 1), 2))), Pow(2, Div(1, 2)))), 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.

2019-09-19 20:12:49.583742 UTC