Theorems · Theorem · commutative algebra
Polynomial.Chebyshev.two_mul_T_eq_U_sub_U
∀ (R : Type u_1) [inst : CommRing R] (n : ℤ), 2 * Polynomial.Chebyshev.T R (n + 2) = Polynomial.Chebyshev.U R (n + 2) - Polynomial.Chebyshev.U R n
- Defined in
- Mathlib.RingTheory.Polynomial.Chebyshev
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 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.
Cites10
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
- Polynomial.Xproof · cited by 1,639
- pow_oneproof · cited by 894
- Polynomial.Chebyshev.Tstatement and proof · cited by 108
- Polynomial.Chebyshev.Ustatement and proof · cited by 71
- Polynomial.Chebyshev.T_eq_U_sub_X_mul_Uproof · cited by 4
- Polynomial.Chebyshev.T_eq_X_mul_U_sub_Uproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.U_eq_two_mul_T_add_Uproof · cited by 1