Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\binom{2n}{n}$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913364279558144 |
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| author | Segun, Akerele Olofin |
| author_facet | Segun, Akerele Olofin |
| contents | We find various series that involves the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function $_pF_q$ 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 $ζ(2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\binom{2n}{n}$ Segun, Akerele Olofin Number Theory Combinatorics 40A05, 11B39, 11B65, 05A10 We find various series that involves the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function $_pF_q$ 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 $ζ(2)$. |
| title | Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\binom{2n}{n}$ |
| topic | Number Theory Combinatorics 40A05, 11B39, 11B65, 05A10 |
| url | https://arxiv.org/abs/2405.16814 |