# Determining a meromorphic function by its poles.

Given a series of complex numbers $$\{a_j\}_{j\in\mathbb{Z}}$$, there exists a meromorphic function having simple poles only at all $$\mathbb{Z}$$ with the residues equal to $$\{a_j\}_{j\in\mathbb{Z}}$$ correspondingly.

Is there any formula to find an analytic expression of this function as a product in terms of these poles with their corresponding residues?