  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 gives solutions in different regions of external
momenta simultaneously. Moreover, it is a technique whereby the difficulties
associated with performing parametric integrals in the standard approach are
transferred to a simpler solving of a system of linear algebraic equations,
thanks to the polynomial character of the relevant integrands. We employ this
method to evaluate a scalar integral for a massless two-loop three-point vertex
with all the external legs off-shell, and consider several special cases for
it, yielding results, even for distinct simpler diagrams. We also consider the
possibility of NDIM in non-covariant gauges such as the light-cone gauge and do
some illustrative calculations, showing that for one-degree violation of
covariance (i.e., one external, gauge-breaking, light-like vector $n_{\mu}$)
the ensuing results are concordant with the ones obtained via either the usual
dimensional regularization technique, or the use of principal value
prescription for the gauge dependent pole, while for two-degree violation of
covariance --- i.e., two external, light-like vectors $n_{\mu}$, the
gauge-breaking one, and (its dual) $n^{\ast}_{\mu}$ --- the ensuing results are
concordant with the ones obtained via causal constraints or the use of the
so-called generalized Mandelstam-Leibbrandt prescription.
