HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS

1998/06/05 by J. A. M. VERMASEREN, J. A. M. Vermaseren · 14 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Feynman integral #Harmonic #Inverse #Mathematical functions and polynomials #Mellin inversion theorem #Mellin transform #Polynomial and algebraic computation #Series (stratigraphy) #Set (abstract data type) #Transformation (genetics) #hep-ph

paper · pdf · doi:10.1142/s0217751x99001032

published as Int.J.Mod.Phys.A14:2037-2076,1999 · 31 pages LaTeX, for programs, see http://norma.nikhef.nl/~t68/summer

arxiv created 1998/06/05 · openalex publication_date 1999/05/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

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.

Cited by

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• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: First moments in N=4 SYM and non-singlet QCD
• Hypergeometric representation of a four-loop vacuum bubble
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• Subleading logarithmic QED initial state corrections to e+e−→γ⁎/Z0⁎ to O(α6L5)
• Hadronic top-quark pair production with NNLL threshold resummation