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Differential Equations of Order Two with One Singular Point

โœ Scribed by Raimundas Vidunas

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
463 KB
Volume
28
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

The goal of this paper is to describe the set of polynomials r โˆˆ C[x] such that the linear differential equation y = ry has Liouvillian solutions, where C is an algebraically closed field of characteristic 0. It is known that the differential equation has Liouvillian solutions only if the degree of r is even. Using differential Galois theory we show that the set of such polynomials of degree 2n can be represented by a countable set of algebraic varieties of dimension n + 1. Some properties of those algebraic varieties are proved.

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