F. Link, Robert, Moments of Discrete Probability Distributions Derived Using Finite Difference Operators, American statistician , 35(1), 1981, pp. 44-46
Formulas for the moments of the better known probability distribution functions are available in the literature on the subject.Persons wishing to derive these formulas, however, may find standard methods to be quite laborious.For discrete probability functions, surprisingly compact and elegant derivations may be obtained by using finite difference operators.Examples of this approach are presented.