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The solution of some integral equations and their connection with dual integral equations and series

Published online by Cambridge University Press:  18 May 2009

J. C. Cooke
J. C. Cooke
Affiliation:
University of Bristol
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The equations. We shall solve the equation

giving the solution in two forms, and give a new solution of

originally solved by Carlemann.

The latter will be extended to the case where the limits are a and b with a < x <b.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 1 , January 1970 , pp. 9 - 20
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

1.Carlemann, T., Über die Abelsche Integralgleichung mit konstanten Integrationsgrenzen, Math. Z. 15 (1922), 111–120.CrossRefGoogle Scholar
2.Durran, J. H. and Lord, W. T., Royal Aircraft Establishment Tech. Note No. Aero 2591 (1958).Google Scholar
3.Copson, E. T., On the problem of the electrified disc, Proc. Edinburgh Math. Soc. (2) 8 (1947), 14–19.CrossRefGoogle Scholar
4.Mikhlin, S., Integral Equations (New York, 1957).CrossRefGoogle Scholar
5.Lundgren, T. and Chiang, D., Solution of a class of singular integral equations, Quart. Appl. Math. 24 (1966), 303–313.CrossRefGoogle Scholar
6.Tranter, C. J., A note on dual equations with trigonometrical kernels, Proc. Edinburgh Math. Soc. (2) 13 (1962), 267–268.CrossRefGoogle Scholar
7.Tranter, C. J., Dual trigonometric series, Proc. Glasgow Math. Assoc. 4 (1959), 49–57.CrossRefGoogle Scholar
8.Tranter, C. J., An improved method for dual trigonometric series, Proc. Glasgow Math. Assoc. 6 (1964), 136–140.CrossRefGoogle Scholar