Theorems · Theorem · global analysis

FormalMultilinearSeries.derivSeries_apply_diag

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  (p : FormalMultilinearSeries 𝕜 E F) (n : ℕ) (x : E),
  ((p.derivSeries n) fun x_1 => x) x = (n + 1) • (p (n + 1)) fun x_1 => x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Analytic

Cited by

2 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace