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The equality of the moduli of certain ratios occurring in the connexion formulae of solutions of some transcendental differential equations

Published online by Cambridge University Press:  24 October 2008

J. Heading
J. Heading
Affiliation:
University College of Wales, Aberystwyth
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Abstract

The differential equations governing the propagation of waves of electric and magnetic types in a plane stratified isotropic plasma are suitably generalized, and we investigate the possibility of models for which the moduli of the reflexion coefficients are identical for the two modes. First, the models are examined without the necessity of finding general solutions, and, secondly, by using the circuit relations for the hypergeometric functions occurring in the explicit solutions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 347 - 361
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Bateman, H.Higher transcendental functions, Volume I. (McGraw Hill, New York; 1953).Google Scholar
(2)Budden, K. G.Radio waves in the ionosphere (Cambridge, 1961)Google Scholar
(3)Heading, J. Theoretical ionospheric radio propagation, Ph.D. Dissertation (Cambridge, 1953)Google Scholar
(4)Heading, J.Composition of reflection and transmission formulae. J. Res. Nat. Bur. Standards Sect. D, 67 (1963), 65–77.Google Scholar
(5)Heading, J.Refractive index profiles based on the hypergeometric equation and the confluent hypergeometric equation. Proc. Cambridge Philos. Soc. 61 (1965), 897–913.CrossRefGoogle Scholar
(6)Heading, J.Polarisation of obliquely reflected waves from an isotropic plane-stratified plasma. Radio Sci. 4 (1969), 441–447.CrossRefGoogle Scholar
(7)Heading, J. and Whipple, R. T. P.The oblique reflexion of long wireless waves from the ionosphere at places where the earth's magnetic field is regarded as vertical. Philos. Trans. Roy. Soc. London Ser. A 244 (1952), 469–503.Google Scholar
(8)Kamke, E.Differentialgleichungen Lösungsmethoden und Lösungen: Gewöhnlichen Differentialgleichungen (Chelsea; New York, 1959).Google Scholar
(9)Westcott, B. S.Exact solutions for vertically polarized electromagnetic waves in horizontally stratified isotropic media. Proc. Cambridge Philos. Soc. 66 (1969), 675–684.CrossRefGoogle Scholar