  In this paper, we propose a new method for evaluating scalar one-loop Feynman
integrals in generalized D-dimension. The calculations play an important
building block for two-loop and higher-loop corrections to the processes at
future colliders such as the Large Hadron Collider (LHC) and the International
Linear Collider (ILC). In this method, scalar one-loop N-point functions will
be presented as the one-fold Mellin-Barnes representation of (N-1)-point ones
with shifting space-time dimension. This representation offers a clear
advantage that we can construct recursively the analytic expressions for
N-point functions from the basic ones which are one-point functions. The
compact formulae for scalar one-loop two-point functions with massive internal
lines and three-point, four-point functions with massless internal lines are
given as examples in this article. In particular, they are written in terms of
generalized hypergeometric series such as Gauss, Appell F 1 functions. We also
perform a sample numerical check for the analytical expressions in this report
by comparing with LoopTools and AMBRE/MB. We find that the numerical results
from this work are in good agreement with LoopTools at $\epsilon^0$ -expansion
and AMBRE/MB at higher-order of $\epsilon$-expansion, at higher D-dimension.
