Talk:Weierstrass factorization theorem

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Typos

Hi! there are typos: it should be as follows

Then there exists an entire function that has (only) zeroes at every point of {zi}; in particular, P is such a function1:

   P(z)=\prod_{i=1}^\infty E_{p_i}\left(\frac{z}{z_i}\right).

I doubt that this statement is correct:

 *
         The theorem may be generalized  ..... respectively;

then: f(z)=\frac{\prod_i(z-z_i)}{\prod_j(z-p_j)}.

Why should any of these products converge?

cu , F

Clean-up needed

Article says:

Holomorphic functions can be factored: If f is a function holomorphic in a region,

\Omega

, with zeroes at every point of

\lbrace z_{i}\rbrace _{i}\subset \mathbb {C} -\{0\}

then there exists an entire function g, and a sequence…

What is $\Omega$ ? Simply connected? Are the zeroes in $\Omega$ ? (where else!) Are they simple zeroes or multiple? I really doubt that the statement, has it stands now, is correct. Everything would be fine if $\Omega =\mathbf {C}$ and if the zeroes allow multiplicity, but I don't know what the editor really meant. --Bdmy (talk) 18:37, 10 April 2009 (UTC)[reply]

Cosine formula

Is the cosine formula correct? I only ask because it goes to zero when z=0. Psalm 119:105 (talk) 11:12, 20 August 2009 (UTC)[reply]

You're right, there was a mistake in the formula. I removed the \pi z factors. - Greg

Examples of factorization

In the right hand of both examples there are exponentials lacking.

It would be nice to give an example when the entire function does not have any zero (some exponential). —Preceding unsigned comment added by 163.10.1.186 (talk) 17:41, 21 October 2009 (UTC)[reply]