Sums of products of the Coulomb wave functions over degenerate manifolds ha
ve been obtained in a closed form. These sums appear in many atomic and mol
ecular problems. The sums have been obtained making use of the properties o
f the Coulomb Green's function G(r, r', E), in the limit E --> E-n, where E
-n, is the eigenenergy of the hydrogenlike atomic ion. The closed Hostler-P
ratt form of G in the coordinate representation has been used. The sums cal
culated are a consequence of the n degeneracy of the Coulomb atomic energy
levels. This itself, as is well known, follows from the four-dimensional sy
mmetry of the Coulomb problem for the hydrogen atom.