Editing Weierstrass factorization theorem (section)

{{Short description|Theorem in complex analysis that entire functions can be factorized according to their zeros}}
In [[mathematics]], and particularly in the field of [[complex analysis]], the '''Weierstrass factorization theorem''' asserts that every [[entire function]] can be represented as a (possibly infinite) product involving its [[Zero of a function|zeroes]].  The theorem may be viewed as an extension of the [[fundamental theorem of algebra]], which asserts that every polynomial may be factored into linear factors, one for each root.

The theorem, which is named for [[Karl Weierstrass]], is closely related to a second result that every sequence tending to infinity has an associated entire function with zeroes at precisely the points of that sequence.

A generalization of the theorem extends it to [[meromorphic function]]s and allows one to consider a given meromorphic function as a product of three factors: terms depending on the function's [[zeros and poles]], and an associated non-zero [[holomorphic function]].{{citation needed|date=April 2019}}