The Coulomb Green's function and multiphoton calculations

The general properties of the Coulomb Green's function are presented, together with its available compact integral representations and discrete state expansions. These representations are most useful as they provide elegant and efficient ways to compute 'exact' values of high-order perturbative matrix elements in hydrogen. Such calculations are of interest as they represent accurate benchmark data for multiphoton transition probabilities. Recent applications involving the Coulomb Green's function for the Dirac equation are also reviewed.