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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The differential equation $ Q=0$ in which $ Q$ is a quadratic form in $ y'',y',y$ having meromorphic coefficients


Author: Roger Chalkley
Journal: Proc. Amer. Math. Soc. 116 (1992), 427-435
MSC: Primary 34A20; Secondary 34A05, 34C20
DOI: https://doi.org/10.1090/S0002-9939-1992-1112488-7
MathSciNet review: 1112488
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Abstract: A simple necessary and sufficient condition is given for the solutions of $ Q = 0$ to be free of movable branch points. And, when the condition is satisfied, all the solutions of $ Q = 0$ can be obtained by solving linear differential equations of order $ \leq 2$. There are four mutually exclusive cases. We shall relate Case 4 to less convenient conditions P. Appell had introduced. We shall also show how Cases 3 and 4 together motivated our discovery of an identity that is essential for a satisfactory theory of relative invariants for homogeneous linear differential equations.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1112488-7
Article copyright: © Copyright 1992 American Mathematical Society