New Analytical Expressions for the Levi-Civita Symbol and Its Treatment as a Generalized Function
W. Astar
TL;DR
This paper derives new analytical expressions for the Levi-Civita symbol using Kronecker delta, extending to higher dimensions and demonstrating its treatment as a generalized function through mathematical and computational validation.
Contribution
It introduces novel analytical formulas for the Levi-Civita symbol applicable in multiple dimensions and shows how to treat it as a generalized function.
Findings
Derived expressions up to 3 dimensions and extended to higher dimensions.
Validated the expressions in Matlab for 5 dimensions.
Concluded the Levi-Civita symbol can be treated as a generalized, discrete function.
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
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications