We have in complex analysis the famous Weierstrass factorization theorem which says that every entire function can be written
$$f(z) = z^ne^{g(z)}\prod_{k=0}^\infty E_{p_n} \left(\frac{z}{a_n}\right)$$
Now to the question, what happens if we do $z=\sin(w)$ or maybe $z = \exp(iw)$?
Will this still be able to represent something useful?