Geodesic
Time-harmonic “complex source” wavefields and their sources in real space
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 131-149 
A. M. Tagirdzhanov; A. S. Blagovestchenskii; A. P. Kiselev. Time-harmonic “complex source” wavefields and their sources in real space. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 131-149. http://geodesic.mathdoc.fr/item/ZNSL_2014_422_a6/
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     title = {Time-harmonic {\textquotedblleft}complex source{\textquotedblright} wavefields and their sources in real space},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper concerns the complexified Green function of the 3D Helmholtz equation in the free space, which is interesting as an exact solution demonstrating Gaussian-beam behavior. This function involves a square root and satisfies an inhomogeneous Helmholtz equation, the right-hand side of which depends on the cut and on the branch of the root. We deal with the explicit description of this generalized function.

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