English
The cuspFunction is analytic at q = 0 whenever n ≠ 0 and the modular form data satisfy the hypotheses; particularly, cuspFunction n f is analytic at 0.
Русский
К cuspFunction относится аналитичность в нуле при n ≠ 0 и удовлетворении условий модулярной формы; cuspFunction n f аналитична в 0.
LaTeX
$$$\text{AnalyticAt}_{\mathbb{C}}(\text{cuspFunction } n\, f, 0)$$$
Lean4
/-- The `q`-expansion of a level `n` modular form, bundled as a `PowerSeries`. -/
def qExpansion : PowerSeries ℂ :=
.mk fun m ↦ (↑m.factorial)⁻¹ * iteratedDeriv m (cuspFunction n f) 0