  By introducing an auxiliary parameter, we find a new representation for
Feynman integrals, which defines a Feynman integral by analytical continuation
of a series containing only vacuum integrals. The new representation therefore
conceptually translates the problem of computing Feynman integrals to the
problem of performing analytical continuations. As an application of the new
representation, we use it to construct a novel reduction method for multi-loop
Feynman integrals, which is expected to be more efficient than known
integration-by-parts reduction method. Using the new method, we successfully
reduced all complicated two-loop integrals in $gg\to HH$ process and $gg\to
ggg$ process.
