Equivalence of recurrence relations for Feynman integrals with the same total number of external and loop momenta

We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R−1)-loop propagator-type integrals. Using this property we solve recurrence relations for 2-loop massless vertex diagrams, with arbitrary numerators and integer powers of propagators in the case when two legs are on the light cone, by reducing the problem to the well-known solution of the corresponding recurrence relations for massless 3-loop propagator diagrams with specific boundary conditions.