The Classical Moment Problem And Some Related Questions In Analysis Access

For the Hamburger problem, this condition is also sufficient (a theorem of Hamburger, 1920): A sequence $(m_n)$ is a Hamburger moment sequence if and only if the Hankel matrix is positive semidefinite.

$$ x P_n(x) = P_n+1(x) + a_n P_n(x) + b_n P_n-1(x) $$ For the Hamburger problem, this condition is also

$$ S(z) = \int_\mathbbR \fracd\mu(x)x - z, \quad z \in \mathbbC\setminus\mathbbR $$ For the Hamburger problem