Maxentropic solution of fractional moment problems

The problem of reconstructing a function from the knowledge of a few of its moments is a special case of the problem inverting an integral transform when there are finitely many data points. The classical method of maximum entropy and the method of maximum entropy in the mean are well suited to attack these problems. What is interesting is that when we are free to choose the data points, the choice can be made to improve the quality of the reconstruction when the method of maximum entropy is used too. In this note we review how to apply these methods and compare them in a couple of examples.