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Series representations of positive integral powers of pi

General Mathematics 2024-05-22 v1

Abstract

Using a pointwise version of Fej\'{e}r's theorem about Fourier series, we obtain two formulae related to the series representations of positive integral powers of π\pi. We also check the correctness of our formulae by the applications of the R software.

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Cite

@article{arxiv.2405.12248,
  title  = {Series representations of positive integral powers of pi},
  author = {Mingzhou Xu},
  journal= {arXiv preprint arXiv:2405.12248},
  year   = {2024}
}

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7 pages