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arXiv · hep-ph/9810241

Harmonic Sums and Mellin Transforms up to two-loop Order

J. Blümlein·S. Kurth
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Abstract

A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ 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 scattering cross sections for space and time-like momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.

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J. Blümlein, S. Kurth. 2000-08-31. Harmonic Sums and Mellin Transforms up to two-loop Order. https://doi.org/10.1103/physrevd.60.014018

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