  The closed form integral representation for the projection onto the subspace
spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The
projection operator onto the $n^2$ dimensional subspace corresponding to the
$n$-th eigenvalue in the Coulomb discrete spectrum is also represented as the
combination of Laguerre polynomials of $n$-th and $(n-1)$-th order. The latter
allows us to derive an analog of the Christoffel-Darboux summation formula for
the Laguerre polynomials. The representations obtained are believed to be
helpful in solving the breakup problem in a system of three charged particles
where the correct treatment of infinitely many bound states in two body
subsystems is one of the most difficult technical problems.
