Coulomb-Sturmian matrix elements of the Coulomb Green's operator (4 pages)

The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal--i.e., Jacobi-matrix form. This Jacobi-matrix structure involves a continued-fraction representation for the inverse of the Green's matrix. The continued fraction can be transformed to a ratio of two {sub 2}F{sub 1} hypergeometric functions. From this result we find an exact analytic formula for the matrix elements of the Green's operator of the Coulomb Hamiltonian.