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Invariants for reducible systems of meromorphic differential equations

Published online by Cambridge University Press:  20 January 2009

W. Balser ,
W. B. Jurkat  and
D. A. Lutz
W. Balser
Affiliation:
Universität UlmD. 7900 UlmWest Germany
W. B. Jurkat
Affiliation:
University of Wisconsin-MilwaukeeMilwaukee Wisconsin 53261
D. A. Lutz
Affiliation:
Syracuse UniversityNew York 13210
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With differential equations in the neighbourhood of an irregular singular point, it sometimes happens that formal solutions may converge. For example, this occurs for Bessel's equation at∞ when the parameter is half of an odd integer. In addition, there are some classical theorems of Perron and Lettenmeyer which give sufficient conditions for the existence of linearly independent analytic solutions at (generally) an irregular singular point. Using the principle of reduction of order, such a solution may be used to transform the differential equation into one whose coefficient matrix is triangularly blocked with an (n – 1) and 1-block on the diagonal. The solutions of the given differential equation can thus be obtained by solving a lower dimensional differential equation plus quadrature.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 2 , June 1980 , pp. 163 - 186
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

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