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Fungrim entry: a92c1a

E4 ⁣(τ)=1+30∑m=1∞cos⁡2 ⁣(πmτ)+1sin⁡4 ⁣(πmτ)E_{4}\!\left(\tau\right) = 1 + 30 \sum_{m=1}^{\infty} \frac{\cos^{2}\!\left(\pi m \tau\right) + 1}{\sin^{4}\!\left(\pi m \tau\right)}
Assumptions:τ∈H\tau \in \mathbb{H}
TeX:
E_{4}\!\left(\tau\right) = 1 + 30 \sum_{m=1}^{\infty} \frac{\cos^{2}\!\left(\pi m \tau\right) + 1}{\sin^{4}\!\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
Sum∑nf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Coscos⁡(z)\cos(z) Cosine
Piπ\pi The constant pi (3.14...)
Sinsin⁡(z)\sin(z) Sine
Infinity∞\infty Positive infinity
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("a92c1a"),
    Formula(Equal(EisensteinE(4, tau), Add(1, Mul(30, Sum(Div(Add(Pow(Cos(Mul(Mul(Pi, m), tau)), 2), 1), Pow(Sin(Mul(Mul(Pi, m), tau)), 4)), For(m, 1, Infinity)))))),
    Variables(tau),
    Assumptions(And(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.

2021-03-15 19:12:00.328586 UTC