Square of an infinite sum

  1. Char. Limit

    Char. Limit 1,986
    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 8,390
    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 1,986
    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!
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