This question is from Ponnusamy Silvermann's Complex analysis section Mittag-Leffler Theorem and I am struck on this.
Derive Weierstrass product theorem from Mittag-Leffler theorem
I am confused on how I should prove it as Mittag-Leffler theorem guarantees the existence of a meromorphic function which has poles at a sequence ${b_n}$ while Weierstrass theorem is about proving existence of an entire function that has zeroes at a sequence of points.
So, if I take a sequence $a_n$ that has no finite limits points. I am not sure how I can use Mittag-Leffler theorem to prove the existence of an entire function which has zeroes only at $a_n$, in fact I don't have any intution.
Can you please help in proving it.