Fungrim symbol: EisensteinG

Symbol: EisensteinG —

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

— Eisenstein series

The Eisenstein series

G_{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
`EisensteinG`	$G_{k}\!\left(\tau\right)$	Eisenstein series
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series

Source code for this entry:

Entry(ID("9bb960"),
    SymbolDefinition(EisensteinG, EisensteinG(k, tau), "Eisenstein series"),
    Description("The Eisenstein series", EisensteinG(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 EisensteinG appears in 3 topics:

Eisenstein series (in 22 entries)
Weierstrass elliptic functions (in 2 entries)
Pi (in 1 entries)

Entries using this symbol

The symbol EisensteinG appears in 23 entries: