Analytic continuation of Mellin transforms up to two-loop order

The analytic continuation of the Mellin transforms to complex values of N f or the basic functions g(i) (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 scatter ing 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 fo ur, where the basis-set g(i) (x) consists of products of Nielsen integrals up to transcendentality four, The computer code ANCONT is provided. (C) 200 0 Elsevier Science B.V. All rights reserved.