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Fungrim entry: 7b62e4

E2 ⁣(τ)=112m=11cos ⁣(2πmτ)1E_{2}\!\left(\tau\right) = 1 - 12 \sum_{m=1}^{\infty} \frac{1}{\cos\!\left(2 \pi m \tau\right) - 1}
Assumptions:τH\tau \in \mathbb{H}
E_{2}\!\left(\tau\right) = 1 - 12 \sum_{m=1}^{\infty} \frac{1}{\cos\!\left(2 \pi m \tau\right) - 1}

\tau \in \mathbb{H}
Fungrim symbol Notation Short description
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
Sumnf(n)\sum_{n} f(n) Sum
Coscos(z)\cos(z) Cosine
Piπ\pi The constant pi (3.14...)
Infinity\infty Positive infinity
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(EisensteinE(2, tau), Sub(1, Mul(12, Sum(Div(1, Sub(Cos(Mul(Mul(Mul(2, Pi), m), tau)), 1)), For(m, 1, Infinity)))))),
    Assumptions(And(Element(tau, HH))))

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2021-03-15 19:12:00.328586 UTC