On the coefficients of power sums of arithmetic progressions

2015/01/08 by András Bazsó, Bazsó, András, István Mező +1
Mathematics · #11B25 #11B68 #11B73 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B25 #msc:11B68 #msc:11B73

paper · pdf · doi:10.48550/arxiv.1501.01843

arxiv created 2015/01/08 · openalex publication_date 2015/01/08 · arxiv updated 2015/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the coefficients of the polynomial S_m,rⁿ(ℓ)=rⁿ+(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.

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