2019/02/28 by Jakob Ablinger, Ablinger, Jakob · 2 citations
Computer Science · Mathematics · #05A10 #11M32 #68W30 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Symbolic Computation (cs.SC) #cs.SC #math.CO #math.NT #msc:05A10 #msc:11M32 #msc:68W30
paper · pdf · doi:10.48550/arxiv.1902.11001
22 pages
arxiv created 2019/04/10 · arxiv updated 2019/04/11
We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of π, log(2) or zeta values. In order to perform these simplifications, we view the series as specializations of generating series. For these generating series, we derive integral representations in terms of root-valued iterated integrals or directly in terms of cyclotomic harmonic polylogarithms. Using substitutions, we express the root-valued iterated integrals as cyclotomic harmonic polylogarithms. Finally, by applying known relations among the cyclotomic harmonic polylogarithms, we derive expressions in terms of several constants. The methods are implemented in the computer algebra package HarmonicSums.