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$q$-expansion of the Eisenstein series $E_4$
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Numbers
$n$
$a_n$
INPUT{numbers.yaml} (not shown in preview)
Definition
This list contains the coefficients of the Eisenstein series $E_4(\tau)$ [1] in its $q$-expansion, $E_4 = \sum_{n=0}^{\infty} a_n q^n$, where $q = e^{2\pi i\tau}$.
Parameters
$n$
—   integer ($n \geq 0$)
Formulas
(1)
$E_4(\tau) = 1 + 240 \sum_{n=1}^\infty \frac{n^3q^n}{1-q^n}$.
Note that different authors use different normalizations for Eisenstein series. Here, we use the normalization that makes the constant coefficient $a_0 = 1$.
numbers = {n: eisenstein_series_qexp(4,101,