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Asymptotic formulas for solutions of a singular linear ordinary differential equation

Published online by Cambridge University Press:  14 November 2011

Richard C. Gilbert
Richard C. Gilbert
Affiliation:
California State University, Fullerton, Calif., U.S.A.
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Synopsis

By use of the theory of asymptotic expansions for first-order linear systems of ordinary differential equations, asymptotic formulas are obtained for the solutions of an nth order linear homogeneous ordinary differential equation with complex coefficients having asymptotic expansions in a sector of the complex plane. These asymptotic formulas involve the roots of certain polynomials whose coefficients are obtained from the asymptotic expansions of the coefficients of the differential operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 1-2 , 1978 , pp. 57 - 70
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Kogan, V. I. and Rofe-Beketov, F. S.On the question of the deficiency indices of differential operators with complex coefficients. Proc. Roy. Soc. Edinburgh. Sect. A, 72 (1975), 281–298.Google Scholar
2Naimark, M. A.Linear differential operators, Pt II (New York: Ungar, 1968).Google Scholar
3Wasow, W.Asymptotic expansions for ordinary differential equations (New York: Interscience, 1965).Google Scholar