The method of scattering function calculations is presented for the case of a double-layer sphere with homogene-ous core surrounded by a radially inhomogeneous shell with a "power law" behavior of the complex refractive index m = Aρb where ρ=2πr/λ (r is the distance from the particle center, λ is the wavelength); A, b are the complex parameters. The method is a combination of Gegenbouer addition theorem and continuous fraction expansion for the Bessel functions and their logarithmic derivatives.