Some remarks on the ϵ-expansion of dimensionally regulated Feynman diagrams

Abstract Some problems related to the construction of the ϵ-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the ϵ-expansion can be expressed in terms of log-sine integrals related to the polylogarithms. It is shown how the analytic continuation of these functions can be constructed in terms of the generalized Nielsen polylogarithms.