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An analytical approach to analyze the diffraction of an arbitrarily directedcomplex-source beam (CSB) by an acoustically soft or hard semi-infinitecircular cone is presented. The beam is generated by assigning acomplex-valued location to a point source; its waist and direction aredefined by the real and imaginary parts of the source coordinate,respectively. The corresponding scalar boundary-value problem is solved by aspherical-multipole analysis. The solution requires the calculation ofassociated Legendre functions of the first kind for complex-valued argumentswhich turns out to be a non-trivial task. Beside a numerical analysis of thecorresponding algorithms we present numerical results for the totalnear- and scattered far-fields

Spherical-multipole analysis of an arbitrarily directed complex-source beam diffracted by an acoustically soft or hard circular cone