Moment problem

In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure ${\displaystyle \mu }$ to the sequence of moments

${\displaystyle m_{n}=\int _{-\infty }^{\infty }x^{n}\,d\mu (x)\,.}$

More generally, one may consider

${\displaystyle m_{n}=\int _{-\infty }^{\infty }M_{n}(x)\,d\mu (x)\,.}$

for an arbitrary sequence of functions ${\displaystyle M_{n}}$.