Monotonicity and inequalities for the ratios of two Bernoulli polynomials
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914788988157952 |
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| author | Yang, Zhen-Hang Qi, Feng |
| author_facet | Yang, Zhen-Hang Qi, Feng |
| contents | In the article, the authors establish the monotonicity of the ratios \begin{equation*} \frac{B_{2n-1}(t)}{B_{2n+1}(t)}, \quad \frac{B_{2n}(t)}{B_{2n+1}(t)},\quad \frac{B_{2m}(t)}{B_{2n}(t)},\quad \frac{B_{2n}(t)}{B_{2n-1}(t)} \end{equation*} and derive some known and new inequalities of the Bernoulli polynomials $B_n(t)$, the Bernoulli numbers $B_{2n}$, and their ratios such as $\frac{B_{2n+2}}{B_{2n}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monotonicity and inequalities for the ratios of two Bernoulli polynomials Yang, Zhen-Hang Qi, Feng General Mathematics Primary 11B68, Secondary 26D05, 41A60 In the article, the authors establish the monotonicity of the ratios \begin{equation*} \frac{B_{2n-1}(t)}{B_{2n+1}(t)}, \quad \frac{B_{2n}(t)}{B_{2n+1}(t)},\quad \frac{B_{2m}(t)}{B_{2n}(t)},\quad \frac{B_{2n}(t)}{B_{2n-1}(t)} \end{equation*} and derive some known and new inequalities of the Bernoulli polynomials $B_n(t)$, the Bernoulli numbers $B_{2n}$, and their ratios such as $\frac{B_{2n+2}}{B_{2n}}$. |
| title | Monotonicity and inequalities for the ratios of two Bernoulli polynomials |
| topic | General Mathematics Primary 11B68, Secondary 26D05, 41A60 |
| url | https://arxiv.org/abs/2405.05280 |