  For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite
$\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave
function $\chi^\ell_k$ which is a function of three internal coordinates. This
article provides necessary and sufficient constraints on $\chi^\ell_k$ to
ensure that the external wave function $\Psi^\ell_m$ is analytic. These
constraints effectively amount to boundary conditions on $\chi^\ell_k$ and its
derivatives at the boundary of the internal space. Such conditions find
similarities in the (planar) two-body problem where the wave function (to
lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary
conditions to prove useful for constructing singularity free three-body basis
sets for the case of nonvanishing angular momentum.
