Given two power series,
$f(x)=\sum_{n=0}^{\infty}a_{n}x^{n}$
and
$g(x)=\sum_{n=0}^{\infty}b_{n}x^{n}.$
It is easy to form their product
$f(x)g(x)=\sum_{n=0}^{\infty}c_{n}x^{n}$
where
$c_{n}=\sum_{k=0}^{n}a_{k}b_{n-k}.$
But many of the series I come across only contain negative powers of $x$, that is
$h(x)=\sum_{n=0}^{\infty}d_{n}x^{-n}.$
Is there any tricks or methods anyone knows of to find the series representation of the product $f(x)h(x)$ ??