Geodesic
Diffraction of the plane waves on conical obstacles
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 142-154

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The problem of diffraction of a plane wave on conical obstacle of rather orbitrary cross-section is considered. Construction of a solution in the form of the Watson integral and its further investigation allowes to derive some formulas describing spherical waves diffracted by the vertex of a cone. 
@article{ZNSL_1988_173_a12,
     author = {V. P. Smyshlyaev},
     title = {Diffraction of the plane waves on conical obstacles},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {142--154},
     publisher = {mathdoc},
     volume = {173},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a12/}
}
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V. P. Smyshlyaev. Diffraction of the plane waves on conical obstacles. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 142-154. http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a12/