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Integrals of logarithmic functions and alternating multiple zeta values

  • Ce Xu EMAIL logo
Published/Copyright: March 18, 2019
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Abstract

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.

  1. (Communicated by Filippo Nuccio)

Acknowledgement

The author would like to thank the anonymous referee for his/her helpful comments, which improve the presentation of the paper.

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Received: 2017-12-06
Accepted: 2018-04-23
Published Online: 2019-03-18
Published in Print: 2019-04-24

© 2019 Mathematical Institute Slovak Academy of Sciences

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