Let $f:B^{m}\to\mathbb{C}$ be a multivariate function defined by a power series $f(x)=\sum_{\alpha}c_{\alpha}x^{\alpha},\,\,x\in B^{m}$, where $\alpha\in\mathbb{N}^{m+1}$ and $B^{m}=\{x\in\mathbb{R}^{m+1},\,\,||x||<1\}$. If $\sum_{\alpha}c_{\alpha}x^{\alpha}<\infty,\,\forall\,\,x\in B^{m}$, it is true that for each $p\in B^{m}$ there exist $\{d_{\alpha}\}\subset \mathbb{C}$ and a neighborhood $p\in B^{m}$ such that
$f(x)=\sum_{\alpha}d_{\alpha}(x-p)^{\alpha}$