On logarithmic integrals, harmonic sums and variations

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.

arXiv comment129 pages

References in corpus (7)

• The Multiple Zeta Value Data Mine
• Multiple zeta values and Euler sums
• Special Values of Generalized Log-sine Integrals
• On harmonic numbers and nonlinear Euler sums
• Evaluations of Euler type sums of weight $\le$ 5
• Linear relations between logarithmic integrals of high weight and some closed-form evaluations
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Cited by in corpus (5)

• Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series
• Extensions of Euler Type Sums and Ramanujan Type Sums
• MZV evaluation of hypergeometric series
• Explicit Evaluations for Several Variants of Euler Sums
• Distribution evaluation of hypergeometric series