The Z-Transform of the Levi-Civita Symbol

TL;DR

This paper derives the Z-transform of the Levi-Civita symbol up to three dimensions, generalizes it to higher dimensions, and connects it to Laplace transforms via Tustin's transform.

Contribution

It provides a novel derivation and generalization of the Z-transform for the Levi-Civita symbol, linking it to Laplace transforms in a new way.

Findings

Z-transform derived for 3D Levi-Civita symbol

Generalization to higher dimensions achieved

Expressions for Laplace transform obtained

Abstract

A derivation of the Z-transform of the Levi-Civita symbol is carried out up to 3 dimensions, and generalized to higher dimensions. Using its Z-transforms, corresponding expressions for the Laplace transform are also found, using Tustin's transform