Theorems · Theorem · special functions
Polynomial.Chebyshev.eval_T_real_eq_one_iff
∀ {n : ℕ},
n ≠ 0 →
∀ (x : ℝ), Polynomial.eval x (Polynomial.Chebyshev.T ℝ ↑n) = 1 ↔ ∃ k ≤ n, Even k ∧ x = Real.cos (↑k * Real.pi / ↑n)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Unitsproof · cited by 2,804
- Nat.cast_oneproof · cited by 2,501
- Units.valproof · cited by 1,966
- Real.pistatement and proof · cited by 1,774
- Polynomial.evalstatement and proof · cited by 796
- Evenstatement and proof · cited by 444
- Real.cosstatement and proof · cited by 424
- Int.cast_oneproof · cited by 371
- Polynomial.Chebyshev.Tstatement and proof · cited by 108
- abs_oneproof · cited by 87
- Int.negOnePow_evenproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.isLocalMax_T_realproof · cited by 1
- Polynomial.Chebyshev.isMaxOn_T_realproof · cited by 1
- Polynomial.Chebyshev.isExtrOn_T_real_iffproof · cited by 0