Fungrim entry: 3bf702

E_{2}\!\left(\tau\right) = \frac{6}{{\pi}^{2}} \zeta\!\left(\frac{1}{2}, \tau\right)

Assumptions:

\tau \in \mathbb{H}

TeX:

E_{2}\!\left(\tau\right) = \frac{6}{{\pi}^{2}} \zeta\!\left(\frac{1}{2}, \tau\right)

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`Pow`	${a}^{b}$	Power
`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("3bf702"),
    Formula(Equal(EisensteinE(2, tau), Mul(Div(6, Pow(Pi, 2)), WeierstrassZeta(Div(1, 2), tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Eisenstein series

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