Harmonic sums, Mellin transforms and Integrals

This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that are encountered in Feynman diagram calculations. Together with results for the values of the higher harmonic series at infinity the presented algorithms can be used for the symbolic evaluation of whole classes of integrals that were thus far intractable. Also many of the sums that had to be evaluated seem to involve new results. Most of the algorithms have been programmed in the language of FORM. The resulting set of procedures is called SUMMER.Comment: 31 pages LaTeX, for programs, see http://norma.nikhef.nl/~t68/summe

Deep Inelastic Structure Functions at two Loops

We present the analytic calculation of the Mellin moments of the structure functions F_2, F_3 and F_L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F_2, F_3 and F_L. We perform the inverse Mellin transformation analytically and find our results in agreement with earlier calculations in the literature by Zijlstra and van Neerven.Comment: 45 pages LaTe

Deep-inelastic structure functions: Reconstruction from Mellin moments

We summarize the method of calculating Mellin moments of deep-inelastic structure functions in perturbative QCD. We briefly discuss all steps to a complete analytical reconstruction of the perturbative corrrections in x-space.Comment: 6 pages LaTeX, presented at LL2000, Bastei (Germany

A calculation of the three-loop helicity-dependent splitting functions in QCD

We have calculated the complete matrix of three-loop helicity-difference (`polarized') splitting functions Delta P_ik^(2), i,k = q,g, in massless perturbative QCD. In this note we briefly discuss some properties of the polarized splitting functions and our non-standard determination of the hitherto missing lower-row quantities Delta P_gq^(2) and Delta P_gg^(2). The resulting next-to-next-to-leading order (NNLO) corrections to the evolution of polarized parton distributions are illustrated and found to be small even at rather large values of the strong coupling constant alpha_s.Comment: 10 pages, LaTeX (PoS style), 4 eps-figures. Proceedings of `Loops & Legs 2014', Weimar (Germany), April/May 201