Generalized Hausdorff inverse moment problem

We consider a generalization of Hausdorff moment problem in which the inputs are generalized moments defined by μαn≡∫01xn[f(x)]αdx(n=1,2,…) where α is a real number and f(x) is the probability density function to be determined. The necessary and sufficient conditions for the existence of the solution are established. The convergence of the sequence of solutions for the corresponding finite problem, when the number of input moments increases, is also studied. We show how to construct this sequence by using a maximum-entropy principle which is based on Tsallis's family of entropies. The method is illustrated with a number of examples.