Stieltjesmomentenproblem
The Stieltjesmomentenproblem, named after Thomas Joannes Stieltjes, is the problem in analysis and probability of characterizing sequences (m_k)_{k≥0} for which there exists a nonnegative Borel measure μ on the half-line [0, ∞) with moments m_k = ∫_0^∞ x^k dμ(x) for all k. Such a sequence is called a Stieltjes moment sequence and is the moment sequence of a measure supported on [0, ∞). The problem is a special case of the Hamburger moment problem with nonnegative support and is connected to orthogonal polynomials on [0, ∞) and to the Stieltjes transform.
Characterization and criteria: A necessary condition is that all Hankel matrices H_n = (m_{i+j})_{i,j=0}^n are positive semidefinite.
Constructive approaches and tools: If a representing measure exists, one can construct it via orthogonal polynomials
History and context: The problem was developed in the late 19th century by Stieltjes and remains fundamental