 Polynomial-growth Liouville theorem for harmonic functions

If an entire harmonic function on ${\mathbb{R}}^n$ grows like $O(1+|x{|}^{k+\alpha })$ with $k\in \mathbb{N}$ and $0<\alpha <1$, then it is a harmonic polynomial of degree at most $k$. Apply the interior derivative estimate of order $k+1$ on expanding balls.