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Fungrim entry: 23a5e0

G2k ⁣(τ+n)=G2k ⁣(τ)G_{2 k}\!\left(\tau + n\right) = G_{2 k}\!\left(\tau\right)
Assumptions:k∈Z≥1  and⁡  τ∈H  and⁡  n∈Zk \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
TeX:
G_{2 k}\!\left(\tau + n\right) = G_{2 k}\!\left(\tau\right)

k \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
EisensteinGGk ⁣(τ)G_{k}\!\left(\tau\right) Eisenstein series
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
HHH\mathbb{H} Upper complex half-plane
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("23a5e0"),
    Formula(Equal(EisensteinG(Mul(2, k), Add(tau, n)), EisensteinG(Mul(2, k), tau))),
    Variables(k, n, tau),
    Assumptions(And(Element(k, ZZGreaterEqual(1)), Element(tau, HH), Element(n, ZZ))))

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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