Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.derivative_U_eval_one
∀ {R : Type u_1} [inst : CommRing R] (n : ℤ),
3 * Polynomial.eval 1 (Polynomial.derivative (Polynomial.Chebyshev.U R n)) = (↑n + 2) * (↑n + 1) * ↑n- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Polynomialstatement · cited by 5,681
- Finset.prodproof · cited by 2,356
- Finset.rangeproof · cited by 1,341
- Polynomial.evalstatement and proof · cited by 796
- Nat.iterateproof · cited by 740
- Polynomial.derivativestatement and proof · cited by 331
- Finset.prod_singletonproof · cited by 78
- Polynomial.Chebyshev.Ustatement and proof · cited by 71
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.derivative_U_eval_one_dvdproof · cited by 0
- Polynomial.Chebyshev.derivative_U_eval_one_eq_divproof · cited by 0