  We propose two ways for determining the Green's matrix for problems admitting
Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form
on some basis representation. In addition to the recurrence relation comming
from the Jacobi-matrix, the first approach also requires the matrix elements of
the Green's operator between the first elements of the basis. In the second
approach the recurrence relation is solved directly by continued fractions and
the solution is continued analytically to the whole complex plane. Both
approaches are illustrated with the non-trivial but calculable example of the
D-dimensional Coulomb Green's matrix. We give the corresponding formulas for
the D-dimensional harmonic oscillator as well.
