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A note on polynomial expressions for sums of power of integers multiplied by exponential terms. (English) Zbl 1411.11020

Summary: The possible polynomial expressions for sums of powers of integers multiplied by an exponential term are investigated. We explicitly give factorization of these polynomials in terms of the roots of Apostol-Bernoulli polynomials. As a special case, alternating sums of powers of integers are also considered, and some new polynomial expressions are given.

MSC:

11B65 Binomial coefficients; factorials; \(q\)-identities
11B68 Bernoulli and Euler numbers and polynomials
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