Analytic continuation of Mellin transforms up to two-loop order Original Research Article

The analytic continuation of the Mellin transforms to complex values of N for the basic functions gi(x) of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space- and time-like momentum transfer are evaluated. These Mellin transforms provide the analytic continuations of all finite harmonic sums up to the level of the threefold sums of transcendentality four, where the basis-set gi(x) consists of products of Nielsen integrals up to transcendentality four. The computer code ANCONT is provided.