  The central limit for the product of free random variables are studied by
evaluating all the moments of the limit distribution. The logarithm of the
central limit is found to be the same as the sum of two independent free random
variables: one semicircularly distributed and another uniformly distributed.
The logarithm of central limit has a moment-generating function of $\exp(\xi^2
s/2) {_{1}F_{1}}\left(1-s; 2; -\xi^2 s \right)$.
