Square of an infinite sum

Char. Limit

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...

LCKurtz

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.

Char. Limit

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!