1307.3150 (J. S. Dowker)

Poweroids revisited - an old symbolic approach    [PDF]

J. S. Dowker

Jeffery's 1861 computations using finite difference calculus are resurrected and extended from forward differences to general delta operators and used to neatly prove theorems in the Rota--Mullins theory of polynomials of binomial type (Steffensen's poweroids) allowing, for example, compact treatments of umbral composition, the binomial property and the connection constants. It is shown that it forms a legitimate alternative to the usual umbral device and also anticipates a number of results obtained more recently.

View original: http://arxiv.org/abs/1307.3150