TY - CHAP
T1 - Explicit evaluation of certain sums of multiple zeta-star values
AU - Yamamoto, Shuji
PY - 2013
Y1 - 2013
N2 - Bowman and Bradley proved an explicit formula for the sum of multiple zeta values whose indices are the sequence (3, 1, 3, 1, ⋯ , 3, 1) with a number of 2's inserted. Kondo, Saito and Tanaka considered the similar sum of multiple zeta-star values and showed that this value is a rational multiple of a power of p. In this paper, we give an explicit formula for the rational part. In addition, we interpret the result as an identity in the harmonic algebra.
AB - Bowman and Bradley proved an explicit formula for the sum of multiple zeta values whose indices are the sequence (3, 1, 3, 1, ⋯ , 3, 1) with a number of 2's inserted. Kondo, Saito and Tanaka considered the similar sum of multiple zeta-star values and showed that this value is a rational multiple of a power of p. In this paper, we give an explicit formula for the rational part. In addition, we interpret the result as an identity in the harmonic algebra.
KW - Bowman-Bradley theorem
KW - Harmonic algebra
KW - Kondo-Saito-Tanaka theorem
KW - Multiple zeta values
KW - Multiple zeta-star values
UR - http://www.scopus.com/inward/record.url?scp=84892945471&partnerID=8YFLogxK
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U2 - 10.7169/facm/2013.49.2.7
DO - 10.7169/facm/2013.49.2.7
M3 - Chapter
AN - SCOPUS:84892945471
SN - 9788323226550
VL - 49
SP - 283
EP - 289
BT - Functiones et Approximatio, Commentarii Mathematici
PB - Adam Mickiewicz University Press
ER -