Mathlib Map

Theorems · Theorem · special functions

Polynomial.Chebyshev.isMaxOn_T_real

∀ {n k : ℕ},
  n ≠ 0 →
    k ≤ n →
      Even k →
        IsMaxOn (fun x => Polynomial.eval x (Polynomial.Chebyshev.T ℝ ↑n)) (Set.Icc (-1) 1)
          (Real.cos (↑k * Real.pi / ↑n))
Defined in
Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.RootsExtrema
Cited by
1 results in Mathlib
Foundations
Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.Chebyshev.isExtrOn_T_real · cited by 1Chebyshev.isExtrOn_T_realReal · cited by 25697RealReal.pi · cited by 1774Real.piSet.Icc · cited by 1702Set.IccPolynomial.eval · cited by 796Polynomial.evalEven · cited by 444EvenReal.cos · cited by 424Real.cosIsMaxOn · cited by 114IsMaxOnPolynomial.Chebyshev.T · cited by 108Chebyshev.Tabs_le · cited by 64abs_lePolynomial.Chebyshev.abs_eval_T_real_le_one · cited by 7Chebyshev.abs_eval_T_real…isMaxOn_iff · cited by 6isMaxOn_iffPolynomial.Chebyshev.eval_T_real_eq_one_iff · cited by 3Chebyshev.eval_T_real_eq_…Chebyshev.isMaxOn_T_realCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.