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Some Notes on Alternating Power Sums
of Arithmetic Progressions András Bazsó
Institute of Mathematics
University of Debrecen
and
MTA-DE Research Group ``Equations Functions and Curves''
Hungarian Academy of Sciences and University of Debrecen
P. O. Box 400
H-4002 Debrecen
Hungary
mailto:bazsoa@science.unideb.hubazsoa@science.unideb.hu

István Mezo
Department of Mathematics
Nanjing University of Information Science and Technology
No. 219 Ningliu Rd.
Pukou, Nanjing, Jiangsu
PR China
mailto:istvanmezo81@gmail.comistvanmezo81@gmail.com

in

Abstract:

We show that the alternating power sum

$$r^n - \left(m+r\right)^n + \left(2m+r\right)^n - \cdots + (-1)^{\ell-1} \left(\left(\ell-1\right)m + r\right)^n$$

can be expressed in terms of Stirling numbers of the first kind and r-Whitney numbers of the second kind. We also prove a necessary and sufficient condition for the integrality of the coefficients of the polynomial extensions of the above alternating power sum.