Template:Green's function equations for the radiation potential for a dock like structure

[math]\displaystyle{ \phi_n^{\mathrm{R}}(x) = \int_{-L}^{L}G(x,\xi) \left( \alpha\phi_n^{\mathrm{R}}(\xi) - i\omega X_n(\xi) \right)\mathrm{d} \xi }[/math]