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Fungrim entry: ad9ba2

E2k ⁣(i∞)=lim⁡τ→i∞E2k ⁣(τ)=1E_{2 k}\!\left(i \infty\right) = \lim_{\tau \to i \infty} E_{2 k}\!\left(\tau\right) = 1
Assumptions:k∈Z≥1k \in \mathbb{Z}_{\ge 1}
TeX:
E_{2 k}\!\left(i \infty\right) = \lim_{\tau \to i \infty} E_{2 k}\!\left(\tau\right) = 1

k \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
ConstIii Imaginary unit
Infinity∞\infty Positive infinity
ComplexLimitlim⁡z→af(z)\lim_{z \to a} f(z) Limiting value, complex variable
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("ad9ba2"),
    Formula(Equal(EisensteinE(Mul(2, k), Mul(ConstI, Infinity)), ComplexLimit(EisensteinE(Mul(2, k), tau), For(tau, Mul(ConstI, Infinity))), 1)),
    Variables(k),
    Assumptions(And(Element(k, ZZGreaterEqual(1)))))

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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