# Square of an infinite sum

by Char. Limit
Tags: infinite, square
 PF Patron P: 1,930 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...
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P: 6,741
 Quote by 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...
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.
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P: 1,930
 Quote by 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.
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!