
TL;DR
This paper introduces a duality linking the coefficients of the characteristic polynomial of the Maurer-Cartan form of the Wronskian matrix to those of the original differential equation, deriving Abel's identity as a consequence.
Contribution
It establishes a novel duality framework that connects differential equation coefficients with Maurer-Cartan forms, providing a new perspective on Abel's identity.
Findings
Derived a duality matching polynomial coefficients
Revealed a new interpretation of Abel's identity
Connected Maurer-Cartan forms with differential equations
Abstract
We provide a natural duality that matches, in reverse order, the coefficients of the characteristic polynomial of the Maurer-Cartan of the Wronskian matrix with the coefficients of the original differential equation. Abel's identity is recovered as a corollary.
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Taxonomy
TopicsMatrix Theory and Algorithms · Polynomial and algebraic computation · Mathematical functions and polynomials
