Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 079, 14 pages      arXiv:2403.16945      https://doi.org/10.3842/SIGMA.2024.079
Contribution to the Special Issue on Asymptotics and Applications of Special Functions in Memory of Richard Paris

New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values

John M. Campbell a, M. Lawrence Glasser b and Yajun Zhou cd
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

Received March 26, 2024, in final form August 28, 2024; Published online September 03, 2024

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.

Key words: binomial coefficients; cyclotomic multiple zeta values; multiple polylogarithms.

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