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."))