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Physical Mathematics by Kevin Cahill

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9

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Bessel functions

9.1 Bessel functions of the first kind

Friedrich Bessel (1784–1846) invented functions for problems with circular symmetry. The most useful ones are defined for any integer n by the series

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(9.1)

The first term of this series tells us that for small |z| 1

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(9.2)

The alternating signs in (9.1) make the waves ...

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