Recognitions:
Gold Member

## Square of an infinite sum

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...
 PhysOrg.com mathematics news on PhysOrg.com >> Pendulum swings back on 350-year-old mathematical mystery>> Bayesian statistics theorem holds its own - but use with caution>> Math technique de-clutters cancer-cell data, revealing tumor evolution, treatment leads

Recognitions:
Gold Member
Homework Help
 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.

Recognitions:
Gold Member
 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!

 Similar discussions for: Square of an infinite sum Thread Forum Replies Introductory Physics Homework 5 Advanced Physics Homework 4 Advanced Physics Homework 3 Advanced Physics Homework 1 Advanced Physics Homework 15