Fungrim entry: 0701dc

$\eta\!\left(16 i\right) = \frac{1}{{2}^{113 / 64}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 4}}{{\left(1 + \sqrt{2}\right)}^{1 / 16}} {\left(-{2}^{5 / 8} + \sqrt{1 + \sqrt{2}}\right)}^{1 / 2} \eta(i)$
References:
• https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940
TeX:
\eta\!\left(16 i\right) = \frac{1}{{2}^{113 / 64}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 4}}{{\left(1 + \sqrt{2}\right)}^{1 / 16}} {\left(-{2}^{5 / 8} + \sqrt{1 + \sqrt{2}}\right)}^{1 / 2} \eta(i)
Definitions:
Fungrim symbol Notation Short description
DedekindEta$\eta(\tau)$ Dedekind eta function
ConstI$i$ Imaginary unit
Pow${a}^{b}$ Power
Sqrt$\sqrt{z}$ Principal square root
Source code for this entry:
Entry(ID("0701dc"),
Formula(Equal(DedekindEta(Mul(16, ConstI)), Mul(Mul(Mul(Div(1, Pow(2, Div(113, 64))), Div(Pow(Sub(Pow(2, Div(1, 4)), 1), Div(1, 4)), Pow(Add(1, Sqrt(2)), Div(1, 16)))), Pow(Add(Neg(Pow(2, Div(5, 8))), Sqrt(Add(1, Sqrt(2)))), Div(1, 2))), DedekindEta(ConstI)))),
References("https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940"))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC