Sums of Powers of Sine and Generalized Bernoulli Polynomials
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913113001951232 |
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| author | Fairbanks, Leon D. |
| author_facet | Fairbanks, Leon D. |
| contents | We produce formulas for $$\sum_{j=1}^{2^{n-2}}\frac{1}{\sin^s\left(\frac{(2j-1)π}{2^n}\right)}$$ in terms of Generalized Bernoulli and Euler polynomials and use one of the formulas to produce a nice integral representation of the Riemann zeta function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sums of Powers of Sine and Generalized Bernoulli Polynomials Fairbanks, Leon D. General Mathematics 11M06 We produce formulas for $$\sum_{j=1}^{2^{n-2}}\frac{1}{\sin^s\left(\frac{(2j-1)π}{2^n}\right)}$$ in terms of Generalized Bernoulli and Euler polynomials and use one of the formulas to produce a nice integral representation of the Riemann zeta function. |
| title | Sums of Powers of Sine and Generalized Bernoulli Polynomials |
| topic | General Mathematics 11M06 |
| url | https://arxiv.org/abs/2502.15966 |