A mixed spectral method is proposed and analyzed for the Stokes
problem in a semi-infinite channel. The method is based on a
generalized Galerkin approximation with Laguerre-functions in the $x$
direction and Legendre-polynomials in the $y$ direction. The
well-posedness of this method is established by deriving a lower bound
on the {\em inf-sup} constant. Numerical results indicate that the
derived lower bound is sharp. Rigorous error analysis is also carried
out.