Asymptotic behavior of the Fourier coefficients for the problem of scattering on contours $r=(1+\beta\cos\varphi)^\gamma$

In this paper the analytic properties of the wave function in the region bounded by the scattering body are studied. This problem is of major importance for the development of the analytic side of the method of separation of variables in problems with noncoordinate boundaries. New asymptotic estimates for the Fourier coefficients of the scattered field are obtained. They indicate the analyticity of the wave function in the physical plane for all $r>0$.