Double tails of multiple zeta values

P. Akhilesh

doi:10.1016/j.jnt.2016.06.020

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arXiv · 2105.12156

Double tails of multiple zeta values

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.

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P. Akhilesh. 2021-05-25. Double tails of multiple zeta values. https://doi.org/10.1016/j.jnt.2016.06.020

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