Systematization of basic divergent integrals in perturbation theory and renormalization group functions

We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals Ilog(i)(λ2), i=1,2,…,n, λ being the renormalization group scale, which need not be evaluated. Only the coefficients of the basic divergent integrals are show to determine renormalization group functions. Relations between these coefficients of different loop orders are derived.