On One Representation of Analytic Functions by Harmonic Functions

Let $u(x)$ be a function analytic in some neighborhood $\mathcal D$ about the origin, $\mathcal D\subset\Bbb R^n$. We study the representation of this function in the form of a series $u(x)=u_0(x)+|x|^2u_1(x)+|x|^4u_2(x)+\dotsb$, where $u_k(x)$ are functions harmonic in $\mathcal D$. This representation is a generalization of the well-known Almansi formula.