Theorems · Theorem · measure theory
MeasureTheory.taylorWithinEval_charFun_zero
∀ {μ : MeasureTheory.Measure ℝ} [MeasureTheory.IsFiniteMeasure μ] {n : ℕ},
MeasureTheory.MemLp id (↑n) μ →
∀ (t : ℝ),
taylorWithinEval (MeasureTheory.charFun μ) n Set.univ 0 t =
∑ k ∈ Finset.range (n + 1), (↑k.factorial)⁻¹ * (↑t * Complex.I) ^ k * ↑(∫ (x : ℝ), x ^ k ∂μ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Complexstatement · cited by 5,565
- Finset.sumstatement and proof · cited by 5,195
- Set.univstatement and proof · cited by 3,945
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- MeasureTheory.integralstatement and proof · cited by 1,779
- mul_assocproof · cited by 1,667
- Complex.ofRealstatement and proof · cited by 1,654
- Finset.rangestatement and proof · cited by 1,341
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.taylorWithinEval_charFun_two_zeroproof · cited by 1