New sums mixing harmonic numbers and central binomial coefficients
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908816655777792 |
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| author | Bataille, Micheal Frontczak, Robert |
| author_facet | Bataille, Micheal Frontczak, Robert |
| contents | We study two new classes of sums with inverse binomial coefficients and harmonic numbers. In addition we establish recursive solutions to the following power sums \begin{equation*} U_d(n) = \sum_{k=1}^n \frac{2^{2k}}{\binom{2k}{k}} \cdot k^d \quad \mbox{and}\quad V_d(n) = \sum_{k=1}^n \frac{2^{2k}}{\binom{2k}{k}}\cdot k^d\,H_k, \end{equation*} where $d$ is a positive integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New sums mixing harmonic numbers and central binomial coefficients Bataille, Micheal Frontczak, Robert Number Theory 05A10, 11B37, 11B39 We study two new classes of sums with inverse binomial coefficients and harmonic numbers. In addition we establish recursive solutions to the following power sums \begin{equation*} U_d(n) = \sum_{k=1}^n \frac{2^{2k}}{\binom{2k}{k}} \cdot k^d \quad \mbox{and}\quad V_d(n) = \sum_{k=1}^n \frac{2^{2k}}{\binom{2k}{k}}\cdot k^d\,H_k, \end{equation*} where $d$ is a positive integer. |
| title | New sums mixing harmonic numbers and central binomial coefficients |
| topic | Number Theory 05A10, 11B37, 11B39 |
| url | https://arxiv.org/abs/2602.06068 |