# Multiplication of Two series.Anyone?

• April 7th 2010, 09:09 AM
younhock
Multiplication of Two series.Anyone?
Can i simplify [ $\sum_{n=0}^\infty \frac{(-1)^n}{n!}x^{n+1}$ ] [ $\sum_{n=0}^\infty a_nx^n$ ] to $\sum_{n=0}^\infty b_nx^n$ where my $b_n= \frac{(-1)^0}{0!}{a_n}+\frac{(-1)^1}{1!}{a_{n-1}}+\frac{(-1)^2}{2!}{a_{n-2}}+$....... $+\frac{(-1)^n}{n!}{a_0}$ .

Is that true?
• April 7th 2010, 09:18 AM
chisigma
That's almost true... that is 'all right' if You write the product as $x \cdot \sum_{n=0}^{\infty} b_{n}\cdot x^{n}$ ...

Kind regards

$\chi$ $\sigma$