A Pochhammer type sampling reconstruction of analytic functions

We give a characterization of the functions f analytic on the half-plane Re ( z ) > σ that can be expressed in the form f ( z ) = ∑ n = 0 ∞ β n ( − z ) n n ! for some β n ∈ C . It will follow that the β n depend on the values of f on the integers so this gives a sampling reconstruction of these functions. Several examples of this representation are given.