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Some triple integral equations

Published online by Cambridge University Press:  18 May 2009

C. J. Tranter
C. J. Tranter
Affiliation:
Royal Military College of Science, Shrivenham
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Potential problems in which different conditions hold over two different parts of the same boundary can often be conveniently reduced to the solution of a pair of dual integral equations. In some problems, however, the boundary condition is such that different conditions hold over three different parts of the boundary and, in such cases, the integral equations involved are frequently of the form

where f(r), g(r) are specified functions of r, p = ± ½ and ø(u) is to be found. Such equations might well be called triple integral equations and, in this note, I point out certain special cases which I have found to be capable of solution in closed form.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 4 , September 1960 , pp. 200 - 203
Copyright
Copyright © Glasgow Mathematical Journal Trust 1960

References

1.Watson, G. N., Theory of Bessel functions (Cambridge, 1944), (a) p. 401, (b) p. 405.Google Scholar
2.Tranter, C. J., Dual trigonometrical series, Proc. Glasgow Math. Assoc. 4 (1959), 49–57.CrossRefGoogle Scholar
3.Magnus, W. and Oberhettinger, F. (translated by Wermer, J.), Special functions of mathematical physics (New York, 1949),(a) p. 8, (b) p. 53.Google Scholar