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On a family of polynomials related to \(\zeta (2,1)=\zeta (3)\). (English) Zbl 1455.11124
Burgos Gil, José Ignacio (ed.) et al., Periods in quantum field theory and arithmetic. Based on the presentations at the research trimester on multiple zeta values, multiple polylogarithms, and quantum field theory, ICMAT 2014, Madrid, Spain, September 15–19, 2014. Cham: Springer. Springer Proc. Math. Stat. 314, 621-630 (2020).
Summary: 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 [J. M. Borwein et al., Electron. J. Comb. 4, No. 2, Research paper R5, 19 p. (1997; Zbl 0884.40004)].
For the entire collection see [Zbl 1446.81002].
MSC:
11M32 Multiple Dirichlet series and zeta functions and multizeta values
33C47 Other special orthogonal polynomials and functions
Citations:
Zbl 0884.40004
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References:
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