Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.T_derivative_eq_U
∀ {R : Type u_1} [inst : CommRing R] (n : ℤ),
Polynomial.derivative (Polynomial.Chebyshev.T R n) = ↑n * Polynomial.Chebyshev.U R (n - 1)- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 109 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.
Cites39
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 and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Polynomial.Xproof · cited by 1,639
- sub_selfproof · cited by 996
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_Tproof · cited by 1
- Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_Uproof · cited by 1
- Polynomial.Chebyshev.add_one_mul_self_mul_T_eq_poly_in_Tproof · cited by 1
- Polynomial.Chebyshev.T_derivative_mem_span_Tproof · cited by 1
- Polynomial.Chebyshev.derivative_T_eval_oneproof · cited by 0
- Polynomial.Chebyshev.isLocalExtr_T_real_iffproof · cited by 0