General Formula for N-point One-loop Feynman Integrals

The negative dimensional integration method (NDIM) is a technique where several difficulties concerning loop integration can be overcome. From usual covariant gauges to complicated Coulomb gauge integrals, and even the trickiest light-cone integrals one can apply the methodology of NDIM. In this work we show how to construct a general formula – we mean arbitrary exponents of propagators, off-shell external momenta and distinct massive propagators – for one-loop scalar integrals, for {\it covariant} gauges, and apply it to one through six-point loop integrals. We present detailed analysis of pentagon and hexagon scalar integrals for massive/massless internal particles being external momenta on or off mass shell.