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Electromagnetic fields in uniaxial anisotropic media can be obtained based on spherical vector wave functions in isotropic media. Applying the boundary conditions of electromagnetic fields on each interface of an impedance sphere coated with a uniaxial anisotropic layer, the expansion coefficients of electromagnetic fields in the uniaxial anisotropic medium and free space can be derived. The present method is very general, which can be reduced to many isotropic subcases. The present method has been validated in those subcases. Scattering by an impedance sphere with an anisotropic coating is presented and discussed.