“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 calculus is an example of the algebraization of the analysis-here restricted to the algebra of polynomials. Many of the results of ψ-calculus may be extended to Markowsky Q-umbral calculus where Q stands for a generalized difference operator, i.e. the one lowering the degree of any polynomial by one. This is a review article based on the recent first author contributions [1]. As the survey article it is supplemented by the short indicatory glossaries of notation and terms used by Ward [2], Viskov [7, 8], Markowsky [12], Roman [28–32] on one side and the Rota-oriented notation on the other side [9–11, 1, 3, 4, 35] (see also [33]).
@article{bwmeta1.element.doi-10_2478_BF02475976,
author = {Andrzej Kwa\'sniewski and Ewa Borak},
title = {Extended finite operator calculus-an example of algebraization of analysis},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {767-792},
zbl = {1120.05008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475976}
}
Andrzej Kwaśniewski; Ewa Borak. Extended finite operator calculus-an example of algebraization of analysis. Open Mathematics, Tome 2 (2004) pp. 767-792. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475976/
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