Abstract
Explicit expressions are derived for the electric and magnetic fields generated in free space by a given, or assumed, distribution of electric and magnetic currents confined within a finite volume (source region). The fields are expansions of TM and TE spherical modes with additional radial terms, proportional to the respective radial current densities. The obtained expressions do not contain singular terms, satisfy Maxwell's equations both inside and outside the source region, and are suitable for practical numerical calculations ; there is no need to exclude any volume around the observation point. The fields outside the source region are also expansions of TE and TM spherical waves, but without the additional radial terms.

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