Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

According to wikipedia,

"...the Weierstrass factorization theorem in complex analysis, named after Karl Weierstrass, asserts that entire functions can be represented by a product involving their zeroes."

Yet the exponential function is an entire function with no zeros, is there a implicit stipulation in this theorem that entire functions must have at least one zero in order for the theorem to apply?

Note: Maybe this is stupidly obvious, but I wan't to make sure there isn't a more advanced point of view which resolves this by considering points whose real part approaches negative infinity, or something of the like.

share|cite|improve this question
up vote 5 down vote accepted

In the Weierstrass factorization theorem, the product is allowed to have a factor of $e^{g(z)}$ outside, so since the exponential function has no zeros, it is just represented by $e^z$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.