# Definition(s) > [!NOTE] Definition 1 (Exponential Generating Function) > Let $(a_{n})_{n\geq{0}}$ be a [[Sequences|sequence]] in $\mathbb{R}.$ The [[Power Series|formal power series]] $\sum_{n=0}^{\infty} a_{n} \frac{x^{n}}{n!}$is the exponential generating function of $(a_{n})_{n\geq0}.$ > [!Example] Example > Contents # Properties(s) # Application(s) **More examples**: # Bibliography