We denote by $\mathcal{E}$ the set of functions $f : \mathbb{C} \rightarrow \mathbb{C}$ expandable as a power series with radius of convergence infinity. Justify that if $(f, g) \in \mathcal{E}^{2}$ and $(\lambda, \mu) \in \mathbb{C}^{2}$, then $\lambda f + \mu g \in \mathcal{E}$ and $fg \in \mathcal{E}$.