Lamb's general solution arises from the fact that the pressure  satisfies the Laplace equation, and can be expanded in a series of solid spherical harmonics in spherical coordinates.  As a result, the solution to the Stokes equations can be written:
where  and  are solid spherical harmonics of order :
and the  are the associated Legendre polynomials. The Lamb's solution can be used to describe the motion of fluid either inside or outside a sphere.  For example, it can be used to describe the motion of fluid around a spherical particle with prescribed surface flow, a so-called squirmer, or to describe the flow inside a spherical drop of fluid.  For interior flows, the terms with  are dropped, while for exterior flows the terms with  are dropped (often the convention  is assumed for exterior flows to avoid indexing by negative numbers).