Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients \binom2nn

2024/05/27 by Akerele Olofin Segun, Segun, Akerele Olofin
Mathematics · Physics and Astronomy · #05A10 #11B39 #11B65 #40A05 #Advanced Mathematical Identities #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.16814

openalex publication_date 2024/05/27 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

Abstract

We find various series that involves the central binomial coefficients \binom2nn, 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).

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