  A unifying and generalizing approach to representations of the positive-part
and absolute moments $\mathsf{E} X_+^p$ and $\mathsf{E}|X|^p$ of a random
variable $X$ for real $p$ in terms of the characteristic function (c.f.) of
$X$, as well as to related representations of the c.f.\ of $X_+$, generalized
moments $\mathsf{E} X_+^p e^{iuX}$, truncated moments, and the distribution
function is provided. Existing and new representations of these kinds are all
shown to stem from a single basic representation. Computational aspects of
these representations are addressed.
