On the coefficients of power sums of arithmetic progressions

JOURNAL OF NUMBER THEORY

卷:153

Article

Bazso, Andras^1,2  Mezo, Istvan³ 

[1] Hungarian Acad Sci, MTA DE Res Grp Equat Funct & Curves, Inst Math, H-4010 Debrecen, Hungary

[2] Univ Debrecen, H-4010 Debrecen, Hungary

[3] Nanjing Univ Informat Sci & Technol, Dept Math, Nanjing, Jiangsu, Peoples R China

关键词: Arithmetic progressions;    Power sums;    Stirling numbers;    r-Whitney numbers;    Bernoulli polynomials;   

DOI  :  10.1016/j.jnt.2015.01.019

来源: Elsevier

【 摘 要 】

We investigate the coefficients of the polynomial S-m,r(n)(l) = r(n) + (m + r)(n) + (2m + r)(n) + ... + ((l - 1)m + r)(n). We prove that these can be given in terms of Stirling numbers of the first kind and r-Whitney numbers of the second kind. Moreover, we prove a necessary and sufficient condition for the integrity of these coefficients. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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