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?


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