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Title of Journal: J Math Sci

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Abbravation: Journal of Mathematical Sciences

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Springer US

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DOI

10.1007/978-3-540-77345-0

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1573-8795

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On singular points of solutions of linear differen

Authors: S A Abramov D E Khmelnov
Publish Date: 2012/07/29
Volume: 185, Issue: 3, Pages: 347-359
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Abstract

We consider systems of linear ordinary differential equations containing m unknown functions of a single variable x The coefficients of the systems are polynomials over a field k of characteristic 0 Each of the systems consists of m equations independent over kx d/dx The equations are of arbitrary orders We propose a computer algebra algorithm that given a system S of this form constructs a polynomial dx ∈ kx 0 such that if S possesses a solution in barkleft left x alpha right rightm for some alpha in bark and a component of this solution has a nonzero polar part then dα = 0 In the case where k ⊆ ℂ and S possesses an analytic solution having a singularity of an arbitrary type not necessarily a pole at α the equality dα = 0 is also satisfied

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