Fungrim entry: 4af6db

\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
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("4af6db"),
    Formula(Equal(ComplexDerivative(DedekindEta(tau), For(tau, Exp(Div(Mul(Mul(2, Pi), ConstI), 3)))), Mul(Div(Mul(ConstI, Sqrt(3)), 6), DedekindEta(Exp(Div(Mul(Mul(2, Pi), ConstI), 3)))))))

Topics using this entry

Dedekind eta function

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

2021-03-15 19:12:00.328586 UTC