Square of an infinite sum

  1. Char. Limit

    Char. Limit 1,937
    Gold Member

    Given a general, convergent infinite sum, say, one like this:

    [tex]\sum_{n=0}^\infty a_n x^n[/tex]

    Is there a formula for the square of such a sum? I looked at the Cauchy product, but I'd rather not get a double sum as an answer...
  2. jcsd
  3. LCKurtz

    LCKurtz 8,454
    Homework Helper
    Gold Member

    YMMV but I wouldn't call the Cauchy product a double sum. And if you wish to write the result as a power series, you're stuck with it. Those finite inner sums give the coefficients of ##x^n##. It is what it is.
  4. Char. Limit

    Char. Limit 1,937
    Gold Member

    Aww, well I guess if I need to use the Cauchy product I'll have to figure out how to use it... thanks for the help though!
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?