Abstract:
A generalization of the identity of dimensionless regularization,
$\int d^{D}k(k^2)^{-\alpha}=0$, $\alpha\ne D/2$
is proposed. The generalization is used to divide the complete set of dimensionally
(and analytically) regularized Feynman integrals with one external momentum into
classes of equal integrals, and also for calculating some of them. A nontrivial
symmetry of the propagator integrals is revealed, on the basis of which a complete
system of functional equations for determining two-loop integrals is derived.
Possible generalizations of these equations are discussed.