Extended finite operator calculus-an example of algebraization of analysis
“A Calculus of Sequences” started in 1936 by Ward constitutes the general scheme for extensions of classical operator calculus of Rota-Mullin considered by many afterwards and after Ward. Because of the notation we shall call the Ward's calculus of sequences in its afterwards elaborated form-a ψ-calculus. The ψ-calculus in parts appears to be almost automatic, natural extension of classical operator calculus of Rota-Mullin or equivalently-of umbral calculus of Roman and Rota. At the same time this...