Solutions for a massless off-shell two-loop three-point vertex

Negative dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method simultaneously gives solutions in different regions of external momenta. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals --- the standard approach --- are transferred to a simpler solving of a system of linear algebraic equations. Employing this method, we calculate a massless two-loop three point vertex with all the external legs off-shell. Then NDIM approach allows us to obtain twenty-one distinct new power series representations for the integral in question. In order to verify the correctness of our results, we consider five particular cases where either two of the external legs are put on-shell, or one of them amputated or one exponent of the propagators is set to zero, and compare our results thus obtained with the ones calculated with standard methods in positive dimension.