On some combinations of multiple zeta-star values

2009/12/10 by Kohtaro Imatomi, Imatomi, Kohtaro, Tatsushi Tanaka +5
Mathematics · #11M32 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M32

paper · pdf · doi:10.48550/arxiv.0912.1951

14 pages

arxiv created 2010/04/21 · arxiv updated 2010/04/22

Abstract

We prove that the sum of multiple zeta-star values over all indices inserted two 2's into the string (\underbrace3,1, ..., 3,1_2n) is evaluated to a rational multiple of powers of π². We also establish certain conjectures on evaluations of multiple zeta-star values observed by numerical experiments.

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