Sums of powers of integers and hyperharmonic numbers
2021 ◽
Vol 27
(2)
◽
pp. 101-110
Keyword(s):
In this paper, we obtain a new formula for the sums of k-th powers of the first n positive integers, Sk(n), that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the hyperharmonic numbers, we generalize this formula to the sums of powers of an arbitrary arithmetic progression. Furthermore, we express the Bernoulli polynomials in terms of hyperharmonic polynomials and Stirling numbers of the second kind. Finally, we extend the obtained formula for Sk(n) to negative values of n.
Keyword(s):
Keyword(s):
2009 ◽
Vol 05
(04)
◽
pp. 625-634
2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
◽
2021 ◽
Vol 3
(2)
◽
pp. 92-100