Double tails of multiple zeta values

P. Akhilesh

doi:10.1016/j.jnt.2016.06.020

Double tails of multiple zeta values

Number Theory 2021-05-27 v1

Authors: P. Akhilesh

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Abstract

In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula $\zeta(2)=3\sum_{m=1}^\infty m^{-2}\left({2m\atop m}\right)^{-1}$ to all multiple zeta values, as well as a new and very efficient algorithm for computing these values.

Keywords

multiple zeta values double tails recurrence relations euler formula computation algorithm

Cite

@article{arxiv.2105.12156,
  title  = {Double tails of multiple zeta values},
  author = {P. Akhilesh},
  journal= {arXiv preprint arXiv:2105.12156},
  year   = {2021}
}

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