(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is it possible to describe some infinite degree polynomials by their roots in a way analagous to finite degree polynomials?

2. Relevant equations

3. The attempt at a solution

I know that, since not all infinite degree polynomials have roots (e.g. the power series representation of e^x), it would not be possible to do so for all of them. But what about polynomials like the power series of sin(x)? I was thinking maybe

[tex]\prod^\infty_{n=0} \left ( x^2 - n^2\pi^2 \right )[/tex]

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# Homework Help: Infinite polynomials

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