Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

Journal of Mathematical Physics

Volumn 54, Issue 8, 2013, Pages

  Ablinger, Jakob ^a   Blümlein, Johannes ^b   Schneider, Carsten ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b DESY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84883438724     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4811117     Document Type: Article

References (145)

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143. In general, relations containing sums of logarithmic growth such as S1(n) can be also formally utilized in asymptotic expansions. However, in the following only convergent sums are considered.
144. In http://www.risc.jku.at/research/combinat/software/HarmonicSums/ all relations are available up to weight four. The most involved calculation is the alphabet xi ∈ {1, -1, 1/2, -1/2, 2, -2}; the relations are obtained executing ComputeSSumInfBasis4,{1,-1,1/2,-1/2,2,-2},ExtendAlphabet→True in about 36 hours.
145. Obviously, the xi must be chosen from a subfield of R which is computable, in particular which can be treated within the computer algebra system Mathematica.