  We derive new formulas for the fundamental solutions of slow, viscous flow,
governed by the Stokes equations, in a half-space. They are simpler than the
classical representations obtained by Blake and collaborators, and can be
efficiently implemented using existing fast solvers libraries. We show, for
example, that the velocity field induced by a Stokeslet can be annihilated on
the boundary (to establish a zero slip condition) using a single reflected
Stokeslet combined with a single Papkovich-Neuber potential that involves only
a scalar harmonic function. The new representation has a physically intuitive
interpretation.
