  For loop integrals, the standard method is reduction. A well-known reduction
method for one-loop integrals is the Passarino-Veltman reduction. Inspired by
the recent paper [1] where the tadpole reduction coefficients have been solved,
in this paper we show the same technique can be used to give a complete
integral reduction for any one-loop integrals. The differential operator method
is an improved version of the PV-reduction method. Using this method, analytic
expressions of all reduction coefficients of the master integrals can be given
by algebraic recurrence relation easily. We demonstrate our method explicitly
with several examples.
