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Fungrim entry: df3334

Symbol: EisensteinE Ek ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
The normalized Eisenstein series Ek ⁣(τ)E_{k}\!\left(\tau\right) is defined for even integers k2k \ge 2 and τ\tau in the upper half-plane.
The functions Gk ⁣(τ)G_{k}\!\left(\tau\right) and Ek ⁣(τ)E_{k}\!\left(\tau\right) are the same up to a normalizing factor.
Definitions:
Fungrim symbol Notation Short description
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
EisensteinGGk ⁣(τ)G_{k}\!\left(\tau\right) Eisenstein series
Source code for this entry:
Entry(ID("df3334"),
    SymbolDefinition(EisensteinE, EisensteinE(k, tau), "Normalized Eisenstein series"),
    Description("The normalized Eisenstein series", EisensteinE(k, tau), "is defined for even integers", GreaterEqual(k, 2), "and", tau, "in the upper half-plane."),
    Description("The functions", EisensteinG(k, tau), "and", EisensteinE(k, tau), "are the same up to a normalizing factor."))

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2019-08-19 14:38:23.809000 UTC