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Homework Help: Infinite polynomials

  1. Feb 5, 2008 #1
    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]
  2. jcsd
  3. Feb 5, 2008 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    There's no such thing as an infinite degree polynomial. I presume you mean a power series.

    If (the analtyic continuation) of your power series is actually meromorphic, then there is a general factorization theorem. See:

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