By polynomial formula $(\sum_{i\in m} x_i)^n=\sum_{\substack{j_i \in \mathbb{Z}^+ \\ \sum j_i=n}}\left(\begin{array}{c} n\\ j_{0},\ldots , j_{m-1} \end{array}\right)\prod_{i \in m} x_i^{j_i}$ where $n \in \mathbb{N}$
But what about $n \not \in \mathbb{N}$? For example $(a+b+c)^{\sqrt{3}}$? These cases probably do not have polynomial formula, but do these cases have a infinite sum like a polynomial formula?