Determination of s-ordered moments and moment generating function from quadrature distributions

The sampling functions needed to reconstruct from quadrature distributions both the s-ordered moments of the field and the generalized moment generating function are determined. The sampling function in the latter case turns out to be surprisingly simple. It is proportional to the well-known pattern function f(0k) needed to reconstruct from homodyne data the density matrix element rho(0k) in the Fock basis. As a by-product a useful sum relation for the pattern functions f(mn) is found.