X-Nico

Cylindrical harmonics

where $I\; n(z)$ and $K\; n(z)$ are modified Bessel functions.

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The term cylindrical harmonics is also used to refer to the Bessel functions (that are cylindrical harmonics in the sense described above).

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where $J\; n(z)$ and $Y\; n(z)$ are ordinary Bessel functions.

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It can be seen that the Z(k,z) functions are the kernels of the Fourier transform or Laplace transform of the Z(z) function and so k may be a discrete variable for periodic boundary conditions, or it may be a continuous variable for non-periodic boundary conditions.

see also