Analytic “Lagrange” interpolation for a countably infinite set of points?

There is this theorem:

Given two sequences $z_n$ and $w_n$ of complex numbers such that $|z_n| to infty$, there exists a holomorphic function $f$ such that $f(z_n) = w_n$ for all $n$.

It is a consequence of the Weierstrass factorization theorem and the Mittag-Leffler theorem.

See this question.

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