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

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