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Constructing Stieltjes classes for M-indeterminate absolutely continuous probability distributions

If P is a moment-indeterminate probability distribution, then it is desirable to present explicitly other distributions possessing the same moments as P. In this paper, a method to construct an infinite family of probability densities called the Stieltjes class all with the same moments is presented. The method is applicable for densities with support (0,∞) which satisfy the lower bound: f(x) ≥ A exp{−ax} for some A > 0, a > 0 and some α ∈ (0, 1/2).