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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 079, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.079 (Mi sigma2081) 		 
New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values

John M. Campbella, M. Lawrence Glasserb, Yajun Zhoucd

a Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 4R2, Canada
b Department of Physics, Clarkson University, Potsdam NY 13699, USA
c Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, NJ 08544, USA
d Academy of Advanced Interdisciplinary Studies (AAIS), Peking University, Beijing 100871, P.R. China
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DOI: https://doi.org/10.3842/SIGMA.2024.079
Abstract: Through the application of an evaluation technique based on cyclotomic multiple zeta values recently due to Au, we solve open problems on inverse binomial series that were included in a 2010 analysis textbook by Chen.
Keywords: binomial coefficients; cyclotomic multiple zeta values; multiple polylogarithms.
Funding agency Grant number
U.S. Department of Energy
J.M.C. gratefully acknowledges support by a Killam Postdoctoral Fellowship from the Killam Trusts and wants to thank Karl Dilcher for useful feedback related to the sums investigated in this article. The research of Y.Z. was supported in part by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4).
Received: March 26, 2024; in final form August 28, 2024; Published online September 3, 2024
Document Type: Article
MSC: 33B30, 11B65, 11M32
Language: English
Citation: John M. Campbell, M. Lawrence Glasser, Yajun Zhou, “New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values”, SIGMA, 20 (2024), 079, 14 pp.
Citation in format AMSBIB
\Bibitem{CamGlaZho24}
\by John~M.~Campbell, M.~Lawrence~Glasser, Yajun~Zhou
\paper New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values
\jour SIGMA
\yr 2024
\vol 20
\papernumber 079
\totalpages 14
\mathnet{http://mi.mathnet.ru/sigma2081}
\crossref{https://doi.org/10.3842/SIGMA.2024.079}
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