Theorems · Theorem · harmonic analysis
fourierCoeffOn_eq_integral
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {a b : ℝ} (f : ℝ → E) (n : ℤ) (hab : a < b),
fourierCoeffOn hab f n = (1 / (b - a)) • ∫ (x : ℝ) in a..b, (fourier (-n)) ↑x • f x- Defined in
- Mathlib.Analysis.Fourier.AddCircle
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by5
Results whose statement or proof uses this declaration.
- fourierCoeffOn_of_hasDeriv_rightproof · cited by 1
- bernoulliFourierCoeff_zeroproof · cited by 1
- fourierCoeff_liftIco_eqproof · cited by 1
- fourierCoeff_liftIoc_eqproof · cited by 1
- fourierCoeffOn_congr_aeproof · cited by 0