Let $\mu_n = \langle x^n \rangle$ and $\kappa_n$ be the moments and cumulants of a probability density function $p(x)$.
Given a finite number of the moments, $\mu_1, \dots, \mu_N$, or equivalently a finite number of the cumulants $\kappa_1, \dots, \kappa_N$, I want to approximate the probability density function $p(x)$. The approximation should improve as $N$ increases.
Is there an approximation scheme that allows me to reconstruct $p(x)$ from a finite number of moments with this property?
