Wronskians and Linear Dependence of Formal Power Series
Keith Ball, Cynthia Parks, Wai Yan Pong
TL;DR
This paper presents a new proof showing that the vanishing of generalized Wronskians indicates linear dependence among formal power series, extending results to quotients of germs of analytic functions.
Contribution
It provides a novel proof linking Wronskian vanishing to linear dependence, applicable to formal power series and germs of analytic functions.
Findings
Vanishing generalized Wronskians imply linear dependence.
Results extend to quotients of germs of analytic functions.
New proof simplifies understanding of Wronskian criteria.
Abstract
We give a new proof of the fact that the vanishing of generalized Wronskians implies linear dependence of formal power series in serveral variables. Our results are also valid for quotients of germs of analytic functions.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Combinatorial Mathematics · Mathematical Dynamics and Fractals