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The Quarterly Journal of Mechanics and Applied Mathematics 1950 3(4):411-419; doi:10.1093/qjmam/3.4.411
© 1950 by Oxford University Press
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ON SOME DUAL INTEGRAL EQUATIONS OCCURRING IN POTENTIAL PROBLEMS WITH AXIAL SYMMETRY

C. J. TRANTER

( Military College of Science Shrivenham )

The use of a Hankel transform can reduce the solution of Laplace's equation in cylindrical coordinates (p, z) in the region 0 < p < {infty}, 0 < z < h when the boundary condition on z = 0 is a ‘mixed’ one and that on z = h is of the usual type to the solution of the dual integral equations

Formula
where G(µ), g(p) are given functions of the variables indicated and f(µ) is to be found. A formal solution of these equations is given and, as an example, the solution is applied to find the potential due to a circular disk at constant potential placed with its plane parallel to, and equidistant from, two carthed parallel plates.


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