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The Stokes phenomenon and certain nth-order differential equations II. The Stokes phenomenon

Published online by Cambridge University Press:  24 October 2008

J. Heading
J. Heading
Affiliation:
West Ham College of TechnologyLondon, E. 15
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Extract

1. Introduction. In paper I(2), solutions have been found for the nth-order differential equations (I, 3), (I, 9), (I, 18), namely,

where ϑ = wd/dw, m is any rational fraction and a any constant. Power-series solutions have been found for these equations, together with integral representations and their asymptotic expressions valid for restricted ranges of arg z. The object of this second paper is to consider these asymptotic solutions in more detail, and to extend these expressions to all values of arg z. The Stokes phenomenon will be manifest throughout, and this will be treated in a manner suitable for further application.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 419 - 441
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Airey, J. R.Phil. Mag. (7) 24 (1937), 521.CrossRefGoogle Scholar
(2)Heading, J.Proc. Camb. Phil. Soc. 53 (1957), 399.CrossRefGoogle Scholar
(3)Jeffreys, H. and Jeffreys, B.Methods of mathematical physics, 3rd ed. (Cambridge, 1956).Google Scholar
(4)Miller, J. C. P.Proc. Camb. Phil. Soc. 48 (1952), 243.CrossRefGoogle Scholar
(5)Miller, J. C. P.Tables of Weber parabolic cylinder functions (London, 1955).Google Scholar
(6)Stokes, G. G.Trans. Camb. Phil. Soc. 10 (1864), 106.Google Scholar
(7)Watson, G. N.A treatise on the theory of Bessel functions, 2nd ed. (Cambridge, 1944).Google Scholar