In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence { mn : n = 1, 2, 3, ... }, does there exist a positive Borel measure μ on the real line such that
In other words, an affirmative answer to the problem means that { mn : n = 0, 1, 2, ... } is the sequence of moments of some positive Borel measure μ.
The Stieltjes moment problem, Vorobyev moment problem, and the Hausdorff moment problem are similar but replace the real line by [0, +∞) (Stieltjes and Vorobyev; but Vorobyev formulates the problem in the terms of matrix theory), or a bounded interval (Hausdorff).
Read more about Hamburger Moment Problem: Characterization, Further Results
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