Recognition: unknown
A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
read the original abstract
In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums and generalized harmonic sums emerge as special cases of so-called d'Alembertian solutions of recurrence relations. We show that harmonic sums form a quasi-shuffle algebra and describe a method how we can find algebraically independent harmonic sums. In addition, we define a differentiation on harmonic sums via an extended version of the Mellin transform. Along with that, new relations between harmonic sums will arise. Furthermore, we present an algorithm which rewrites certain types of nested sums into expressions in terms of harmonic sums. We illustrate by nontrivial examples how these algorithms in cooperation with the summation package Sigma support the evaluation of Feynman integrals.
This paper has not been read by Pith yet.
Forward citations
Cited by 2 Pith papers
-
The four-loop non-singlet splitting functions in QCD
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
-
The photon-energy spectrum in $B\to X_s\gamma$ to N$^3$LO: light-fermion and large-$N_{\rm c}$ corrections
N3LO calculation of the B to Xs gamma photon spectrum including complete light-fermion corrections, two massive fermion loops, and large-Nc terms, with improved results in kinetic and MSR mass schemes.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.