Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.T_add_two
∀ (R : Type u_1) [inst : CommRing R] (n : ℤ), Polynomial.Chebyshev.T R (n + 2) = 2 * Polynomial.X * Polynomial.Chebyshev.T R (n + 1) - Polynomial.Chebyshev.T R n
- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 101 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- 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
- Polynomial.Xstatement and proof · cited by 1,639
- pow_oneproof · cited by 894
- Nat.cast_addproof · cited by 586
- sub_add_cancelproof · cited by 344
- neg_add_revproof · cited by 236
- Polynomial.Chebyshev.Tstatement and proof · cited by 108
- neg_add_cancel_commproof · cited by 17
Cited by20
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.T_negproof · cited by 8
- Polynomial.Chebyshev.T_sub_oneproof · cited by 8
- Polynomial.Chebyshev.T_derivative_eq_Uproof · cited by 7
- Polynomial.Chebyshev.degree_Tproof · cited by 7
- Polynomial.Chebyshev.T_eval_negproof · cited by 4
- Polynomial.Chebyshev.T_complex_cosproof · cited by 3
- Polynomial.Chebyshev.T_eval_oneproof · cited by 3
- Polynomial.Chebyshev.T_sub_twoproof · cited by 2
- Polynomial.Chebyshev.U_eq_X_mul_U_add_Tproof · cited by 2
- Polynomial.Chebyshev.T_mul_Tproof · cited by 2
- Polynomial.Chebyshev.T_add_oneproof · cited by 2
- Polynomial.Chebyshev.T_eval_zeroproof · cited by 2