A note on polynomial expressions for sums of power of integers multiplied by exponential terms

The possible polynomial expressions for sums of powers of integers multiplied by an exponential term areinvestigated. 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 aregiven.

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