For $n \in \mathbb{N}$, calculate $\left\|T_n\right\|_{L^\infty([-1,1])}$. The sequence of polynomials $\left(T_n\right)_{n \in \mathbb{N}}$ is defined by $T_0 = 1, T_1 = X$ and $\forall n \in \mathbb{N}, T_{n+2} = 2X T_{n+1} - T_n$.
For $n \in \mathbb{N}$, calculate $\left\|T_n\right\|_{L^\infty([-1,1])}$.
The sequence of polynomials $\left(T_n\right)_{n \in \mathbb{N}}$ is defined by $T_0 = 1, T_1 = X$ and $\forall n \in \mathbb{N}, T_{n+2} = 2X T_{n+1} - T_n$.