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A simple recursive representation of the Faulhaber series

History and Overview 2025-01-27 v1

Abstract

We present a simple elementary recursive representation of the so called Faulhaber series k=1nkN\sum_{k=1}^n k^N for integer nn and NN, without reference to Bernoulli numbers or polynomials.

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Cite

@article{arxiv.2501.13548,
  title  = {A simple recursive representation of the Faulhaber series},
  author = {Dietmar Pfeifer},
  journal= {arXiv preprint arXiv:2501.13548},
  year   = {2025}
}

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93 pages