Theorems · Theorem · special functions
Polynomial.Chebyshev.roots_U_real
∀ (n : ℕ),
(Polynomial.Chebyshev.U ℝ ↑n).roots =
(Finset.image (fun k => Real.cos ((↑k + 1) * Real.pi / (↑n + 1))) (Finset.range n)).val- Cited by
- 2 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites51
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Multisetstatement · cited by 2,627
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Real.pistatement and proof · cited by 1,774
- WithBotproof · cited by 1,498
- LT.lt.ne'proof · cited by 1,417
- Finset.rangestatement and proof · cited by 1,341
- Finset.imagestatement and proof · cited by 910
- one_ne_zeroproof · cited by 885
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.rootMultiplicity_U_realproof · cited by 0
- Polynomial.Chebyshev.isLocalExtr_T_real_iffproof · cited by 0