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Hamburger moment problem

In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence(m0, m1, m2, ...), does there exist a positive Borel measureμ (for instance, the measure determined by the cumulative distribution function of a random variable) on the real line such that mn=∫−∞∞xndμ(x){\displaystyle m_{n}=\int _{-\infty }^{\infty }x^{n}\,d\mu (x)}?In other words, an affirmative answer to the problem means that (m0, m1, m2, ...)

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