Theorems · Theorem · special functions
Polynomial.Chebyshev.integral_measureT_eq_integral_cos
∀ {f : ℝ → ℝ}, ∫ (x : ℝ), f x ∂Polynomial.Chebyshev.measureT = ∫ (θ : ℝ) in 0..Real.pi, f (Real.cos θ)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- MeasureTheory.integralstatement · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Set.Iooproof · cited by 1,214
- one_divproof · cited by 624
- mul_negproof · cited by 590
- intervalIntegralstatement and proof · cited by 546
- Real.sqrtproof · cited by 545
- Real.cosstatement and proof · cited by 424
- Set.uIccproof · cited by 393
- Continuous.continuousOnproof · cited by 311
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zeroproof · cited by 3
- Polynomial.Chebyshev.integral_eval_T_real_measureT_zeroproof · cited by 3
- Polynomial.Chebyshev.integral_measureT_eq_integral_cos_of_continuousproof · cited by 0