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Fungrim entry: 6ade92

θ3 ⁣(0,45i)=[3+5+(3+5+601/4)(2+3)1/3310+105]θ3 ⁣(0,i)\theta_{3}\!\left(0 , 45 i\right) = \left[\frac{3 + \sqrt{5} + \left(\sqrt{3} + \sqrt{5} + {60}^{1 / 4}\right) {\left(2 + \sqrt{3}\right)}^{1 / 3}}{3 \sqrt{10 + 10 \sqrt{5}}}\right] \theta_{3}\!\left(0 , i\right)
References:
  • https://doi.org/10.1016/j.jmaa.2003.12.009
TeX:
\theta_{3}\!\left(0 , 45 i\right) = \left[\frac{3 + \sqrt{5} + \left(\sqrt{3} + \sqrt{5} + {60}^{1 / 4}\right) {\left(2 + \sqrt{3}\right)}^{1 / 3}}{3 \sqrt{10 + 10 \sqrt{5}}}\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
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Source code for this entry:
Entry(ID("6ade92"),
    Formula(Equal(JacobiTheta(3, 0, Mul(45, ConstI)), Mul(Brackets(Div(Add(Add(3, Sqrt(5)), Mul(Add(Add(Sqrt(3), Sqrt(5)), Pow(60, Div(1, 4))), Pow(Add(2, Sqrt(3)), Div(1, 3)))), Mul(3, Sqrt(Add(10, Mul(10, Sqrt(5))))))), 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