Fungrim entry: 1c25d3

\eta'(\tau) = \frac{i}{2 \pi} \eta(\tau) \zeta\!\left(\frac{1}{2}, \tau\right)

Assumptions:

\tau \in \mathbb{H}

TeX:

\eta'(\tau) = \frac{i}{2 \pi} \eta(\tau) \zeta\!\left(\frac{1}{2}, \tau\right)

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`ConstI`	$i$	Imaginary unit
`Pi`	$\pi$	The constant pi (3.14...)
`WeierstrassZeta`	$\zeta\!\left(z, \tau\right)$	Weierstrass zeta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("1c25d3"),
    Formula(Equal(ComplexDerivative(DedekindEta(tau), For(tau, tau)), Mul(Mul(Div(ConstI, Mul(2, Pi)), DedekindEta(tau)), WeierstrassZeta(Div(1, 2), tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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