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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 69, Issue 2


Integrals of logarithmic functions and alternating multiple zeta values

Ce Xu
Published Online: 2019-03-18 | DOI: https://doi.org/10.1515/ms-2017-0227


By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and integrals of logarithmic functions. As applications of these relations, we show that multiple zeta values of the form ζ(1¯,1m1,1¯,1k1),(k,mN)

for m = 1 or k = 1, and ζ(1¯,1m1,p,1k1),(k,mN)

for p = 1 and 2, satisfy certain recurrence relations which allow us to write them in terms of zeta values, polylogarithms and ln 2. Furthermore, we also obtain reductions for certain multiple polylogarithmic values at 12.

MSC 2010: Primary 11A07; Secondary 11M32; 33B15

Keywords: multiple zeta values; multiple polylogarithms; harmonic numbers; Euler sums


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About the article

Received: 2017-12-06

Accepted: 2018-04-23

Published Online: 2019-03-18

Published in Print: 2019-04-24

(Communicated by Filippo Nuccio)

Citation Information: Mathematica Slovaca, Volume 69, Issue 2, Pages 339–356, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0227.

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