New Analytical Expressions for the Levi-Civita Symbol and Its Treatment as a Generalized Function
arXiv:2109.01700
Abstract
New analytical expressions are found for the Levi-Civita symbol using the Kronecker delta symbol. The expressions are derived up to 3 dimensions, extended to higher dimensions, and confirmed in Matlab for 5 dimensions. The expressions can be re-cast in terms of elementary and/or special functions, which lead to the conclusion that the Levi-Civita Symbol can be treated as a generalized, discrete function
This is the 5th version of the manuscript, and wholly supersedes the previous versions. In the previous versions, the generalized function G was sometimes confused with the epsilon itself. In this (fifth) version, it is clarified that G is merely a function used in alternative expressions of the epsilon