Theorems · Theorem · harmonic analysis
Polynomial.fourierCoeff_toAddCircle
∀ (p : Polynomial ℂ) (n : ℤ), fourierCoeff (⇑(Polynomial.toAddCircle p)) n = if 0 ≤ n then p.coeff n.natAbs else 0
The nth Fourier coefficient of a polynomial is the coefficient of X ^ n, or
zero if n < 0.
- Defined in
- Mathlib.Analysis.Polynomial.Fourier
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Polynomialstatement and proof · cited by 5,681
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- add_zeroproof · cited by 2,707
- ContinuousMapstatement · cited by 2,491
- MulZeroClass.mul_zeroproof · cited by 2,091
- Real.pistatement · cited by 1,774
- Polynomial.coeffstatement and proof · cited by 1,045
- map_addproof · cited by 964
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.sum_sq_norm_coeff_eq_circleAverageproof · cited by 1
- Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zeroproof · cited by 0
- Polynomial.fourierCoeff_toAddCircle_natCastproof · cited by 0