I do not know for "the same properties", but Newton series does the trick for a large class of functions.
$$f(x)=g^{[1/2]}(x)=\sum_{m=0}^{\infty} \binom {1/2}m \sum_{k=0}^m\binom mk(-1)^{m-k}g^{[k]}(x)$$
A more extended answer you can find following the link
