On the Green’s function for the Helmholtz operator in an impedance circular cylindrical waveguide

This paper addresses the problem of finding a series representation for the Green’s function of the Helmholtz operator in an infinite circular cylindrical waveguide with impedance boundary condition. Resorting to the Fourier transform, complex analysis techniques and the limiting absorption principle (when the undamped case is analyzed), a detailed deduction of the Green’s function is performed, generalizing the results available in the literature for the case of a complex impedance parameter. Procedures to obtain numerical values of the Green’s function are also developed in this article.