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Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

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Chapter 22APPLICATIONS OF BESSEL FUNCTIONS

22·01.

The majority of applications of Bessel functions are to vibrations of systems with symmetry about an axis; the z coordinate usually either varies little, as in tidal waves on circular sheets of water, or the dependent variable is independent of z. Even if it involves z, Bessel functions usually provide the best treatment if the boundaries are planes of constant z. Bessel functions of order half an odd integer, in combination with Legendre functions, arise in problems of vibration for spherical boundaries. They also occur in various one-dimensional problems, notably the oscillations of a light string loaded with heavy particles at regular intervals, and the transmission of electric waves in a submarine ...

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