On the hyper-sums of powers of integers. (English) Zbl 1399.11062
Summary: The main object of this paper is to study an old problem concerning the hyper-sums of powers of integers. First, we establish some important properties of this problem (generating function, explicit formula, congruence). Finally, an explicit formula for the hyper-sums of powers of integers involving the generalized Bernoulli polynomials are also given.
MSC:
11B73 | Bell and Stirling numbers |
11B68 | Bernoulli and Euler numbers and polynomials |
33C05 | Classical hypergeometric functions, \({}_2F_1\) |