Theorems · Theorem · special functions
Polynomial.Chebyshev.abs_eval_T_real_eq_one_iff
∀ {n : ℕ},
n ≠ 0 → ∀ (x : ℝ), |Polynomial.eval x (Polynomial.Chebyshev.T ℝ ↑n)| = 1 ↔ ∃ k ≤ n, x = Real.cos (↑k * Real.pi / ↑n)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- absstatement and proof · cited by 1,814
- Real.pistatement and proof · cited by 1,774
- le_of_ltproof · cited by 1,175
- one_ne_zeroproof · cited by 885
- Polynomial.evalstatement and proof · cited by 796
- ne_of_gtproof · cited by 637
- div_oneproof · cited by 629
- Real.cosstatement and proof · cited by 424
- mul_nonnegproof · cited by 397
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.eval_T_real_eq_one_iffproof · cited by 3
- Polynomial.Chebyshev.eval_T_real_eq_neg_one_iffproof · cited by 3
- Polynomial.Chebyshev.isExtrOn_T_real_iffproof · cited by 0