Fungrim symbol: EisensteinE

Symbol: EisensteinE —

E_{k}\!\left(\tau\right)

— Normalized Eisenstein series

The normalized Eisenstein series

E_{k}\!\left(\tau\right)

is defined for even integers

k \ge 2

and

\tau

in the upper half-plane.

The functions

G_{k}\!\left(\tau\right)

and

E_{k}\!\left(\tau\right)

are the same up to a normalizing factor.

Definitions:

Fungrim symbol	Notation	Short description
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`EisensteinG`	$G_{k}\!\left(\tau\right)$	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."))

Topics using this symbol

The symbol EisensteinE appears in 6 topics:

Eisenstein series (in 58 entries)
Illustrations of Eisenstein series (in 6 entries)
Modular j-invariant (in 3 entries)
Jacobi theta functions (in 2 entries)
Modular lambda function (in 1 entries)
Dedekind eta function (in 1 entries)

Entries using this symbol

The symbol EisensteinE appears in 68 entries: