norm_mahler_eq — Mathlib

English

The Mahler series mahlerSeries(a) is defined as the continuous map x ↦ ∑' n mahlerTerm(a(n)) n.

Русский

Серия Маhлера mahlerSeries(a) определяется как непрерывное отображение x ↦ ∑' n mahlerTerm(a(n)) n.

LaTeX

$$$$ mahlerSeries(a) = \\sum_{n=0}^{\\infty} mahlerTerm(a(n))\\, n. $$$$

Lean4

/-- The uniform norm of the `k`-th Mahler basis function is 1, for every `k`.
-/
@[simp]
theorem norm_mahler_eq (k : ℕ) : ‖(mahler k : C(ℤ_[p], ℤ_[p]))‖ = 1 := by simp [← mahlerTerm_one]

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