Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions

We prove an Almansi Theorem for quaternionic polynomials %of the form $P(x)=sum_{k=0}^d x^ka_k$ and extend it to quaternionic slice-regular functions. We associate to every such function $f$, a pair $h_1$, $h_2$ of zonal harmonic functions such that $f=h_1-ar x h_2$. We apply this result to get mean value formulas and Poisson formulas for slice-regular quaternionic functions.