An extension of the Abel–Liouville identity
Abstract
In this note, we present an extension of the celebrated Abel–Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characterize the range equivalence of n-dimensional vector-valued functions in the subclass of n-times differentiable functions with a nonvanishing Wronskian.
Keywords
Abel–Liouville identity; generalized Wronskians; complete Bell polynomials
References
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E.T. Bell, Exponential polynomials, Ann. of Math. (2) 35 (1934), no. 2, 258–277.
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G. Teschl, Ordinary Differential Equations and Dynamical Systems, Graduate Studies in Mathematics, 140, American Mathematical Society, Providence, RI, 2012.
Institute of Mathematics, University of Debrecen, Hungary Hungary
https://orcid.org/0000-0003-2382-6035
Department of Mathematics, Faculty of Education, Ain Shams University, Egypt Egypt
amr.zakaria@edu.asu.edu.eg
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