Geodesic
Formal power series and their applications to mathematical theory of diffraction
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 5-16

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The formal power series (FPS) coefficients of which are smooth functions are considered. FPS form an algebra over the field $(\mathbb C)$ of complex numbers. It is possible to differentiate FPS. FPS are series having asymptotic character (in accordance with the definition by V. S. Buslaev and M. M. Scriganov). As an example of applications of FPS we consider the geometro-optical expansion for the scalar analog of Rayleigh waves. 
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     author = {V. M. Babich},
     title = {Formal power series and their applications to mathematical theory of diffraction},
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V. M. Babich. Formal power series and their applications to mathematical theory of diffraction. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 5-16. http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a0/