We denote by $T$ the unique automorphism satisfying, for all $n \in \mathbb{N}$, $T\ell_n = \frac{X^n}{n!}$ and we set $Q = T \circ P \circ T^{-1}$, where $P = L \circ (\alpha I + (1-\alpha)L)^{-1}$.
Show that $Q = D \circ (\alpha I + (1-\alpha)D)^{-1}$. Deduce that $Q$ is a delta endomorphism whose associated polynomial sequence $(r_n)_{n \in \mathbb{N}}$ satisfies
$$\forall n \in \mathbb{N}^*, \quad r_n = \sum_{k=1}^n \binom{n-1}{k-1} \alpha^k (1-\alpha)^{n-k} \frac{X^k}{k!}$$