  We obtain exact formulas for the absolute raw and central moments of the
variance-gamma distribution, as infinite series involving the modified Bessel
function of the second kind and the modified Lommel function of the first kind.
When the skewness parameter is equal to zero (the symmetric variance-gamma
distribution), the infinite series reduces to a single term. Moreover, for the
case that the shape parameter is a half-integer (in our parameterisation of the
variance-gamma distribution), we obtain a closed-form expression for the
absolute moments in terms of confluent hypergeometric functions. As a
consequence, we deduce new exact formulas for the absolute raw and central
moments of the asymmetric Laplace distribution and the product of two
correlated zero mean normal random variables, and more generally the sum of
independent copies of such random variables.
