Analytic continuation of Mellin transforms up to two-loop order

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 g i ( x ) consists of products of Nielsen –integrals up to transcendentalities four.

Abstract

The analytic continuation of the Mellin transforms to complex values of N for\nthe basic functions $g_i(x)$ of the momentum fraction x emerging in the\nquantities of massless QED and QCD up to two-loop order, as the unpolarized and\npolarized splitting functions, coefficient functions, and hard scattering cross\nsections for space- and time-like momentum transfer are evaluated. These Mellin\ntransforms provide the analytic continuations of all finite harmonic sums up to\nthe level of the threefold sums of transcendentality four, where the basis-set\n${g_i(x)}$ consists of products of {\\sc Nielsen}-integrals up to\ntranscendentality four. The computer code {\\tt ANCONT} is provided.\n