We assume $\alpha = 1$. We denote $T_n$ the unique polynomial eigenvector of $\varphi_1$ of degree $n$, of norm 1 (with respect to $S_1$) and with positive leading coefficient. For $n \in \mathbb{N}^*$, determine the roots of $T_n$.
We assume $\alpha = 1$. We denote $T_n$ the unique polynomial eigenvector of $\varphi_1$ of degree $n$, of norm 1 (with respect to $S_1$) and with positive leading coefficient.\\
For $n \in \mathbb{N}^*$, determine the roots of $T_n$.