John M. Campbell, M. Lawrence Glasser, Yajun Zhou, “New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values”, SIGMA, 2024, том 20,079, 14 стр.

New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values

John M. Campbell^a, M. Lawrence Glasser^b, 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

Аннотация: 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.

Ключевые слова: binomial coefficients; cyclotomic multiple zeta values; multiple polylogarithms.

MSC: 33B30, 11B65, 11M32

Поступила: 26 марта 2024 г.; в окончательном варианте 28 августа 2024 г.; опубликована 3 сентября 2024 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2024.079