ar X iv : h ep - t h / 02 05 15 8 v 1 1 5 M ay 2 00 2 Massless and massive one - loop three - point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive , two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time D. Our approach reproduces the known results as well as other solutions as yet unknown in the literature. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.