Abstract
We give a new proof of the identity \(\zeta (\{2,1\}^l)=\zeta (\{3\}^l)\) of the multiple zeta values, where \(l=1,2,\dots \), using generating functions of the underlying generalized polylogarithms. In the course of study we arrive at (hypergeometric) polynomials satisfying 3-term recurrence relations, whose properties we examine and compare with analogous ones of polynomials originated from an (ex-)conjectural identity of Borwein, Bradley and Broadhurst.
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Acknowledgements
The work originated from discussions during the research trimester on Multiple Zeta Values, Multiple Polylogarithms and Quantum Field Theory at ICMAT in Madrid (September–October 2014) and was completed during the author’s visit in the Max Planck Institute for Mathematics in Bonn (March–April 2015); I thank the staff of the institutes for the wonderful working conditions experienced during these visits. I am grateful to Valent Galliano, Erik Koelink, Tom Koornwinder and Slava Spiridonov for valuable comments on earlier versions of the note. I am thankful as well to the two anonymous referees for the valuable feedback on the submitted version.
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Zudilin, W. (2020). On a Family of Polynomials Related to \(\zeta (2,1)=\zeta (3)\). In: Burgos Gil, J., Ebrahimi-Fard, K., Gangl, H. (eds) Periods in Quantum Field Theory and Arithmetic. ICMAT-MZV 2014. Springer Proceedings in Mathematics & Statistics, vol 314. Springer, Cham. https://doi.org/10.1007/978-3-030-37031-2_22
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DOI: https://doi.org/10.1007/978-3-030-37031-2_22
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