A formula giving the known relative invariants for homogeneous linear differential equations
type: Item
instance of: scholarly article
title: A formula giving the known relative invariants for homogeneous linear differential equations
zbMATH Open document ID: 0849.34013
DOI: 10.1016/0022-0396(92)90120-C
author: Roger Chalkley
published in: Journal of Differential Equations
publication date: 1993-04-01T00:00:00Z
review text: Each of the known relative invariants has been found by selecting a suitable combination of particular semi-invariants of the first kind [change of the dependent variable \(y = \rho (z)v]\) in order to obtain an expression that is both a semi-invariant of the first kind and a semi-invariant of the second kind [change of the independent variable \(z = f(\zeta)]\). Because this procedure has been severely limited by computational difficulties, we use results from a previous paper [J. Differ. Equations 80, No. 1, 107-153 (1989; Zbl 0693.34005)] to significantly improve the situation. Our new procedure enables us to verify that, for any integers \(m,s\) satisfying \(3 \leq s \leq 10\) and \(s \leq m\), a certain polynomial given in this paper is a relative invariant of weights \(s\) for homogeneous linear differential equations of order \(m\). This result yields all of the basic relative invariants previously known, and it yields new relative invariants for \(s = 8 \leq m\), \(s = 9 \leq m\), and \(s = 10 \leq m\).
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 147083
zbMATH Keywords: homogeneous
zbMATH Keywords: linear differential equations
zbMATH Keywords: relative invariants
MaRDI profile type: Publication
cites work: Q5532731
cites work: Relative invariants for homogeneous linear differential equations
full work available at URL: 0022-0396(92)90120-c
OpenAlex ID: W2056246194
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description: scientific article; zbMATH DE number 147083