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Bipolar and Toroidal Harmonics

1915
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Proceedings of the Edinburgh Mathematical Society
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Most of the solutions of Laplace's equation in common use in mathematical physics have been expressed in the integral form given by Whittaker,* viz. f 2?r I /(xcos t + y sin t + iz, t) dt. Jo The solutions are well known for which f, regarded as a function of its first argument, is a power, a circular function, a Legendre function of the first or second kind, or a Bessel function. Thus this general form of solution provides a means of classifying known potential functions and of suggesting new

doi:10.1017/s0013091500037494
fatcat:df5ipocnnfadfnmw2hgubd3koi