Template:Incident plane wave in cylindrical coordinates

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Incident potential

The incident potential is a wave of amplitude [math]\displaystyle{ A }[/math] in displacement travelling in the positive [math]\displaystyle{ x }[/math]-direction. The incident potential can therefore be written as

[math]\displaystyle{ \phi^{\mathrm{I}} =e^{k_{0}x}\phi_{0}\left( z\right) =\sum\limits_{n=-\infty}^{\infty} I_{n}(k_{0}r)\phi_{0}\left(z\right) e^{i n \theta} }[/math]