For pt.I, see ibid., vol. 22, no.18 p.L503-9 (1989). A detailed analysis of the Sturmian expansion of the off-shell Coulomb wavefunction is presented. Some analytic properties of the representation are clarified and expressions for the off- and half-shell T matrix and for the near-shell approximation are derived. Finally, an algorithm ensuring rapid and stable calculations of the expansion series is given and extensions to non-Coulombic systems are briefly mentioned.