The Arakawa–Kaneko zeta function

被引：0
作者：
Marc-Antoine Coppo
Bernard Candelpergher
机构：
[1] Nice Sophia Antipolis University,Laboratoire Jean Alexandre Dieudonné
来源：
The Ramanujan Journal | 2010年 / 22卷
关键词：
Poly-Bernoulli numbers; Multiple zeta-star values; Euler sums; Zeta values; 11M41; 11M35; 40-02; 40-03;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present a very natural generalization of the Arakawa–Kaneko zeta function introduced ten years ago by T. Arakawa and M. Kaneko. We give in particular a new expression of the special values of this function at integral points in terms of modified Bell polynomials. By rewriting Ohno’s sum formula, we are able to deduce a new class of relations between Euler sums and the values of zeta.
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页码：153 / 162
页数：9
相关论文
共 6 条
[1]  
Arakawa T.(1999)Multiple zeta values, poly-Bernoulli numbers and related zeta functions Nagoya Math. J. 153 189-209
[2]  
Kaneko M.(2009)Nouvelles expressions des formules de Hasse et de Hermite pour la fonction zeta d’Hurwitz Expo. Math. 27 79-86
[3]  
Coppo M.-A.(1775)Meditationes circa singulare serierum genus Opera Omnia I 15 217-267
[4]  
Euler L.(1997)Poly-Bernoulli numbers J. Theor. Nr. Bordx. 9 199-206
[5]  
Kaneko M.(1999)A generalisation of the duality and sum formulas on the multiple zeta values J. Number Theory 74 39-43
[6]  
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