On logarithmic integrals, harmonic sums and variations
Classical Analysis and ODEs
2020-07-07 v9 Number Theory
Abstract
Based on various non-MZV approaches we evaluate certain logarithmic integrals and harmonic sums. More specifically, 85 LIs, 89 ESs, 263 PLIs, 28 non-alt QESs, 39 GESs, 26 BESs,14 IBESs with weight no more than 5, 193 QLIs, 172 QPLIs, 83 QESs, 7 QBESs, 3 IQBESs with weight no more than 4. With help of MZV theory we evaluate other 10 QESs with weight no more than 4. High weight hypergeometric series, nonhomogeneous integrals and other results are also established.
Cite
@article{arxiv.1911.12155,
title = {On logarithmic integrals, harmonic sums and variations},
author = {Ming Hao Zhao},
journal= {arXiv preprint arXiv:1911.12155},
year = {2020}
}
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129 pages