  We outline an efficient method for the reconstruction of a probability
density function from the knowledge of its infinite sequence of ordinary
moments. The approximate density is obtained resorting to maximum entropy
technique, under the constraint of some fractional moments. The latter ones are
obtained explicitly in terms of the infinite sequence of given ordinary
moments. It is proved that the approximate density converges in entropy to the
underlying density, so that it demonstrates to be useful for calculating
expected values.
