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On Euler's Solution of the simple Difference Equation

History and Overview 2023-09-01 v1

Abstract

In this note we will discuss Euler's solution of the simple difference equation that he gave in his paper{\it ``De serierum determinatione seu nova methodus inveniendi terminos generales serierum"} \cite{E189} (E189:``On the determination of series or a new method of finding the general terms of series") and also present a derivation for the values of the Riemann ζ\zeta-function at positive integer numbers based on Euler's ideas.

Keywords

Cite

@article{arxiv.2308.16312,
  title  = {On Euler's Solution of the simple Difference Equation},
  author = {Alexander Aycock},
  journal= {arXiv preprint arXiv:2308.16312},
  year   = {2023}
}

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11 pages

R2 v1 2026-06-28T12:08:48.277Z