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Fungrim entry: 3bf702

E2 ⁣(τ)=6π2ζ ⁣(12,τ)E_{2}\!\left(\tau\right) = \frac{6}{{\pi}^{2}} \zeta\!\left(\frac{1}{2}, \tau\right)
Assumptions:τH\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
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("3bf702"),
    Formula(Equal(EisensteinE(2, tau), Mul(Div(6, Pow(ConstPi, 2)), WeierstrassZeta(Div(1, 2), tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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

2019-09-19 20:12:49.583742 UTC