English

Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\binom{2n}{n}$

Number Theory 2024-05-28 v1 Combinatorics

Abstract

We find various series that involves the central binomial coefficients (2nn)\binom{2n}{n}, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function pFq_pF_q approach, our method utilizes a straightforward transformation to obtain new evaluations linked to Fibonacci numbers and the golden ratio. Before the end of this paper, we also gave a new series representation for ζ(2)\zeta(2).

Keywords

Cite

@article{arxiv.2405.16814,
  title  = {Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\binom{2n}{n}$},
  author = {Akerele Olofin Segun},
  journal= {arXiv preprint arXiv:2405.16814},
  year   = {2024}
}

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9 pages