  A key issue in the solution of partial differential equations via integral
equation methods is the evaluation of possibly singular integrals involving the
Green's function and its derivatives multiplied by simple functions over
discretized representations of the boundary. For the Helmholtz equation, while
many authors use numerical quadrature to evaluate these boundary integrals, we
present analytical expressions for such integrals over flat polygons in the
form of infinite series. These can be efficiently truncated based on the
accurate error bounds, which is key to their integration in methods such as the
Fast Multipole Method.
