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Fungrim entry: be2f32

η ⁣(8i)=1241/32(21/41)1/2(1+2)1/8η(i)\eta\!\left(8 i\right) = \frac{1}{{2}^{41 / 32}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 2}}{{\left(1 + \sqrt{2}\right)}^{1 / 8}} \eta(i)
References:
  • https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940
TeX:
\eta\!\left(8 i\right) = \frac{1}{{2}^{41 / 32}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 2}}{{\left(1 + \sqrt{2}\right)}^{1 / 8}} \eta(i)
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη(τ)\eta(\tau) Dedekind eta function
ConstIii Imaginary unit
Powab{a}^{b} Power
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("be2f32"),
    Formula(Equal(DedekindEta(Mul(8, ConstI)), Mul(Mul(Div(1, Pow(2, Div(41, 32))), Div(Pow(Sub(Pow(2, Div(1, 4)), 1), Div(1, 2)), Pow(Add(1, Sqrt(2)), Div(1, 8)))), DedekindEta(ConstI)))),
    References("https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940"))

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2019-10-05 13:11:19.856591 UTC