grandes-ecoles 2014 QI.A.1

grandes-ecoles · France · centrale-maths2__mp Roots of polynomials Polynomial evaluation, interpolation, and remainder
Determine $T_0, T_1, T_2$ and $T_3$, where the Chebyshev polynomials of the first kind $(T_n)_{n \in \mathbb{N}}$ are defined by $$\forall n \in \mathbb{N}, \quad \forall \theta \in \mathbb{R}, \quad T_n(\cos\theta) = \cos(n\theta)$$
Determine $T_0, T_1, T_2$ and $T_3$, where the Chebyshev polynomials of the first kind $(T_n)_{n \in \mathbb{N}}$ are defined by
$$\forall n \in \mathbb{N}, \quad \forall \theta \in \mathbb{R}, \quad T_n(\cos\theta) = \cos(n\theta)$$