An approach to the calculation of many-loop massless Feynman integrals

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.