Let $f$ be harmonic functions on the unit disk $\mathbb D$, of the complex plane $\mathbb{C}$. We show that $f$ can be expanded in a series $f=\sum_nf_n$, where $f_n$ is a harmonic function on $\mathbb D_{n,\Gamma,A}$ satisfying $\sup_{z\in\mathbb D_{n,\Gamma,A}}|f_n(z)|\leq C\rho^n$ for some constants $C>0$ and $0<\rho<1$, and where $(\mathbb D_{n,\Gamma,A})_n$ is a suitably chosen sequence of decreasing neighborhoods of the closure of $\mathbb D$. Conversely, if $f$ admits such an expansion then $f$ is of Carleman type. The decrease of the sequence $(\mathbb D_{n,\Gamma,A})_n$ characterizes the smoothness of $f$. These constructions are perfectly explicit.