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Integrals with a large parameter: Hilbert transforms

Published online by Cambridge University Press:  24 October 2008

F. Ursell
F. Ursell
Affiliation:
Department of Mathematics, University of ManchesterM13 9PL
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Abstract

A simple and elegant method of treating one-sided Hilbert transforms

has recently been described by Wong (7). This method immediately gives the form of the expansion but some of the coefficients in the expansion are in an inconvenient form for either analytical or numerical calculation. In the present paper it is shown that these coefficients can be readily determined when the Mellin transform of f(t) is known. The case is treated as an example.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 141 - 149
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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