# Square of an infinite sum

1. Feb 29, 2012

### Char. Limit

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

$$\sum_{n=0}^\infty a_n x^n$$

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. Feb 29, 2012

### 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.

3. Feb 29, 2012

### 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!