  An alternative method is presented for extracting the von Neumann entropy
$-\operatorname{Tr} (\rho \ln \rho)$ from $\operatorname{Tr} (\rho^n)$ for
integer $n$ in a quantum system with density matrix $\rho$. Instead of relying
on direct analytic continuation in $n$, the method uses a generating function
$-\operatorname{Tr} \{ \rho \ln [(1-z \rho) / (1-z)] \}$ of an auxiliary
complex variable $z$. The generating function has a Taylor series that is
absolutely convergent within $|z|<1$, and may be analytically continued in $z$
to $z = -\infty$ where it gives the von Neumann entropy. As an example, we use
the method to calculate analytically the CFT entanglement entropy of two
intervals in the small cross ratio limit, reproducing a result that Calabrese
et al. obtained by direct analytic continuation in $n$. Further examples are
provided by numerical calculations of the entanglement entropy of two intervals
for general cross ratios, and of one interval at finite temperature and finite
interval length.
