Fungrim home page

Fungrim entry: 0701dc

η ⁣(16i)=12113/64(21/41)1/4(1+2)1/16(25/8+1+2)1/2η(i)\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
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("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"))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC