Weierstrass Factorization Theorem is one of the most valuable results to study entire functions:

It is evident that for any finite set of points in the complex plane, we can associate a polynomial p(z) whose zeros are precisely those points in the set. Conversely, as a consequence of the Fundamental Theorem of Algebra, any polynomial function p(z) in the complex plane can be factored as a product containing its zeros.

Weierstrass Factorization Theorem studies what happens when the set of zeros is not finite.