Bounds for the first positive zero of a mixed Bessel function
Journal of Computational and Applied Mathematics
The imaginary zeros of a mixed Bessel function
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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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.