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 measure μ (for instance, the measure determined by the cumulative distribution function of a random variable) on the real line such that m n = ∫ − ∞ ∞ x n d μ ( 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, ...) is the sequence of moments of some positive Borel measure μ.