  The Hamiltonian of a Coulomb plus polynomial potential on the
Coulomb-Sturmian basis has an infinite symmetric band-matrix structure. A band
matrix can always be considered as a block-tridiagonal matrix. So, the
corresponding Green's operator can be given as a matrix-valued continued
fraction. As examples, we calculate the Green's operator for the Coulomb plus
linear and quadratic potential problems and determine the energy levels.
