Theorems · Theorem · commutative algebra

Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_T_eq_poly_in_T

∀ {R : Type u_1} [inst : CommRing R] (n : ℤ),
  (1 - Polynomial.X ^ 2) * (⇑Polynomial.derivative)^[2] (Polynomial.Chebyshev.T R n) =
    Polynomial.X * Polynomial.derivative (Polynomial.Chebyshev.T R n) - ↑n ^ 2 * Polynomial.Chebyshev.T R n

Defined in: Mathlib.RingTheory.Polynomial.Chebyshev
Cited by: 1 results in Mathlib
Foundations: Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_Tproof · cited by 1