Exponential Sequence in the Operational Calculus Model for the n ^TH-Order Forward Difference

Abstract

In the paper, there has been determined an exponential element in the discrete model of the non-classical Bittner operational calculus for the nth-order forward difference.

An Operational Calculus Model with the (m,n) - Symmetric Difference

“…If we define the objects (1), then we have in mind a representation, or a model of the operational calculus. In particular, representations of the operational calculus (1) are discrete models in which the derivative can be understood as: an -order forward difference [16] (2) an -order backward difference [15] (3) or a 2 -order central difference [17] (4)…”

“…For being a constant sequence, representations of operational calculus with derivatives were discussed in [16], [15], [17].…”

“…From Theorem 1 follow difference representations of the Bittner operational calculus mentioned at the beginning of this paper. Namely, for we obtain the model with the forward difference (2) described in [16]. When , we get in turn the model with the central difference (4) constructed in [17].…”