| (Oral Ccp et Centrale) On suppose {\displaystyle\sum\limits_{n\ge0}|a_{n}|\lt\infty}. Donner le rayon de {f(x)=\displaystyle\sum_{n=0}^{+\infty}\dfrac{a_{n}}{n!}x^{n}}. Montrer que {\displaystyle\int_{0}^{+\infty}\!\!\!f(t)\text{e}^{-t}\,\text{d}t=\displaystyle\sum_{n=0}^{+\infty}a_{n}}. |