## Formal power series and their applications in the mathematical theory of diffraction.(English. Russian original)Zbl 1303.78003

J. Math. Sci., New York 194, No. 1, 1-7 (2013); translation from Zap. Nauchn. Sem. POMI 409, 5-16 (2012).
Summary: Formal power series (FPS) the coefficients of which are smooth functions are considered. The FPS form an algebra on the field of complex numbers $$(\mathbb C)$$. One can differentiate the FPS. The FPS are series having an asymptotic nature (in accordance with the definition by V. S. Buslaev and M. M. Skriganov [Teor. Mat. Fiz. 19, 217–232 (1974; Zbl 0291.35020); translation in Theor. Math. Phys. 19(1974), 465–476 (1975; Zbl 0296.35023)]). As an example of applications of the FPS, the geometro-optical expansion for the scalar analog of Rayleigh waves is considered.

### MSC:

 78A45 Diffraction, scattering 35C20 Asymptotic expansions of solutions to PDEs 78M35 Asymptotic analysis in optics and electromagnetic theory

### Citations:

Zbl 0291.35020; Zbl 0296.35023
Full Text:

### References:

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