A group-theory expansion of scalar spherical harmonics is used to obtain an expansion of vector spherical harmonics. This expansion is applied to the multipole-expansion treatment of Mie theory, and explicit expressions suitable for computation of the coefficients of the expansion are obtained. The result is a Mie-theory solution given in the variables and basis vectors of the spherical-coordinate system associated with a Cartesian system that is rotated with respect to the conventionally chosen coordinate system. This result is then used to obtain an analytical-series solution for the power scattered into a conical solid angle centered on any chosen direction from the scattering sphere.
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