Talk:Weierstrass factorization theorem

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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