Fungrim home page

Fungrim entry: 4af6db

η(e2πi/3)=i36η ⁣(e2πi/3)\eta'({e}^{2 \pi i / 3}) = \frac{i \sqrt{3}}{6} \eta\!\left({e}^{2 \pi i / 3}\right)
TeX:
\eta'({e}^{2 \pi i / 3}) = \frac{i \sqrt{3}}{6} \eta\!\left({e}^{2 \pi i / 3}\right)
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("4af6db"),
    Formula(Equal(ComplexDerivative(DedekindEta(tau), tau, Exp(Div(Mul(Mul(2, ConstPi), ConstI), 3))), Mul(Div(Mul(ConstI, Sqrt(3)), 6), DedekindEta(Exp(Div(Mul(Mul(2, ConstPi), ConstI), 3)))))))

Topics using this entry

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

2019-08-19 14:38:23.809000 UTC