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Fungrim entry: 18a4d1

E2 ⁣(τ)=1+6m=11sin2 ⁣(πmτ)E_{2}\!\left(\tau\right) = 1 + 6 \sum_{m=1}^{\infty} \frac{1}{\sin^{2}\!\left(\pi m \tau\right)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
E_{2}\!\left(\tau\right) = 1 + 6 \sum_{m=1}^{\infty} \frac{1}{\sin^{2}\!\left(\pi m \tau\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
Powab{a}^{b} Power
Sinsin ⁣(z)\sin\!\left(z\right) Sine
ConstPiπ\pi The constant pi (3.14...)
Infinity\infty Positive infinity
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("18a4d1"),
    Formula(Equal(EisensteinE(2, tau), Add(1, Mul(6, Sum(Div(1, Pow(Sin(Mul(Mul(ConstPi, m), tau)), 2)), Tuple(m, 1, Infinity)))))),
    Variables(tau),
    Assumptions(And(Element(tau, HH))))

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2019-08-21 11:44:15.926409 UTC