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An Expansion Theorem for a Pair of Singular First Order Equations

Published online by Cambridge University Press:  20 November 2018

S. D. Conte  and
W. C. Sangren
S. D. Conte
Affiliation:
Wayne University
W. C. Sangren
Affiliation:
Oak Ridge National Laboratories
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Titchmarsh (4) has shown how the classical method of complex variables can be used to obtain expansion theorems for the singular cases of the second order equation

(1) .

The purpose of this paper is to indicate how these results can be generalized to the singular cases of the pair of first order equations

,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 554 - 560
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Conte, S. D. and Sangren, W. C., An eigenjunction expansion associated with a pair of first order differential equations, Report, Oak Ridge National Laboratories, 1952.Google Scholar
2. Conte, S. D. and Sangren, W. C., An asymptotic solution for a pair of first order equations, Proc. Amer. Math. Soc, 4 (1953), 696–702.Google Scholar
3. Hurwitz, W., An expansion theorem for a pair of linear first order differential equations. Trans. Amer. Math. Soc, 22 (1921), 526–543.Google Scholar
4. Titchmarsh, E. C., Eigenfunction expansions associated with second order differential equations(Oxford, 1946).Google Scholar