  New types of relationships between Feynman integrals are presented. It is
shown that Feynman integrals satisfy functional equations connecting integrals
with different values of scalar invariants and masses. A method is proposed for
obtaining such relations. The derivation of functional equations for one-loop
propagator- and vertex - type integrals is given. It is shown that a propagator
- type integral can be written as a sum of two integrals with modified scalar
invariants and one propagator massless. The vertex - type integral can be
written as a sum over vertex integrals with all but one propagator massless and
one external momenta squared equal to zero. It is demonstrated that the
functional equations can be used for the analytic continuation of Feynman
integrals to different kinematic domains.
