In mathematics, the trigonometric moment problem is formulated as follows: given a finite sequence {α0, ... αn }, does there exist a positive Borel measure μ on the interval [0, 2π] such that In other words, an affirmative answer to the problems means that {α0, ... αn } are the first n + 1 Fourier coefficients of some positive Borel measure μ on [0, 2π].