We prove the Weierstrass Factorization Theorem. This is a beautiful theorem in complex analysis which states that if we are given an infinite collection of complex numbers (potentially with repetitions) that have no accumulation points and tends to infinity, then every entire function can be expressed as the exponential of an entire function times z^m times an infinite product of Weierstrass elementary factors! This is a classification theorem for entire functions and gives us very useful information about the structure of entire functions.
#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #weierstrass
