A note on harmonic number identities, Stirling series and multiple zeta values

被引：3

作者：

Kuba, Markus ^{[1
]}

Panholzer, Alois ^{[2
]}

机构：

[1] FH Technikum Wien, Dept Appl Math & Phys, Hochstadtpl 6, A-1200 Vienna, Austria

[2] Tech Univ Wien, Inst Diskrete Math & Geometrie, Wiedner Hauptstr 8-10-104, A-1040 Vienna, Austria

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2019年 / 15卷 / 07期

关键词：

Multiple zeta values; multiple zeta star values; Stirling series; Harmonic numbers; Arakawa-Kaneko zeta function; SYMMETRIC FUNCTIONS; MELLIN TRANSFORMS; ARAKAWA; KANEKO; SUMS;

D O I：

10.1142/S179304211950074X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a general type of series and relate special cases of it. to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa-Kaneko zeta function, studied before amongst others by Candelpergher and Coppo, and also by Young. We complement and generalize earlier results. Moreover, we survey properties of certain truncated multiple zeta and zeta star values, pointing out their relation to finite sums of harmonic numbers. We also discuss the duality result of Hoffman, relating binomial sums and truncated multiple zeta star values.

引用

页码：1323 / 1348

页数：26

共 50 条

[31] Identity families of multiple harmonic sums and multiple zeta star values
Zhao, Jianqiang
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2016, 68 (04) : 1669 - 1694
[32] A note on the values of zeta
Kim, T
SMARANDACHE NOTIONS, VOL 12, 2001, 12 : 291 - 294
[33] Summation algorithms for Stirling number identities
Kauers, Manuel
JOURNAL OF SYMBOLIC COMPUTATION, 2007, 42 (10) : 948 - 970
[34] Algorithms for Some Euler-Type Identities for Multiple Zeta Values
Ding, Shifeng
Liu, Weijun
JOURNAL OF APPLIED MATHEMATICS, 2013,
[35] IDENTITIES INVOLVING CYCLIC AND SYMMETRIC SUMS OF REGULARIZED MULTIPLE ZETA VALUES
Machide, Tomoya
PACIFIC JOURNAL OF MATHEMATICS, 2017, 286 (02) : 307 - 359
[36] Transformation on Infinite Double Series and Applications to Harmonic Number Identities
Chu Wenchang
De Donno Livia
Applicable Algebra in Engineering, Communication and Computing, 2005, 15 : 339 - 348
[37] Harmonic number identities via hypergeometric series and Bell polynomials
Liu, Hongmei
Wang, Weiping
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2012, 23 (01) : 49 - 68
[38] Transformation on infinite double series and applications to harmonic number identities
Chu, WC
De Donno, L
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2005, 15 (05) : 339 - 348
[39] Multiple series connected to Hoffman's conjecture on multiple zeta values
Fischler, S.
JOURNAL OF ALGEBRA, 2008, 320 (04) : 1682 - 1703
[40] Note on poly-Bernoulli numbers and multiple zeta values
Kaneko, Masanobu
DIOPHANTINE ANALYSIS AND RELATED FIELDS - DARF 2007/2008, 2008, 976 : 118 - 124

← 1 2 3 4 5 →