For $p \notin \mathbb{N}^*$, $p \neq 0$, let $f(x) = \sum_{n=0}^{+\infty} a_n x^n$ be a non-zero power series solution of $(E_p)$. Using the result of Question 39, deduce finally that the function $f$ is not an element of $E$.
For $p \notin \mathbb{N}^*$, $p \neq 0$, let $f(x) = \sum_{n=0}^{+\infty} a_n x^n$ be a non-zero power series solution of $(E_p)$. Using the result of Question 39, deduce finally that the function $f$ is not an element of $E$.