  We derive an analytic expression for the scalar one-loop pentagon and hexagon
functions which is convenient for subsequent numerical integration. These
functions are of relevance in the computation of next-to-leading order
radiative corrections to multi-particle cross sections. The hexagon integral is
represented in terms of n-dimensional triangle functions and (n+2)-dimensional
box functions. If infrared poles are present this representation naturally
splits into a finite and a pole part. For a fast numerical integration of the
finite part we propose simple one- and two-dimensional integral
representations. We set up an iterative numerical integration method to
calculate these integrals directly in an efficient way. The method is
illustrated by explicit results for pentagon and hexagon functions with some
generic physical kinematics.
