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arXiv · 2502.15966

Sums of Powers of Sine and Generalized Bernoulli Polynomials

Leon D. Fairbanks
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Abstract

We produce formulas for $$\sum_{j=1}^{2^{n-2}}\frac{1}{\sin^s\left(\frac{(2j-1)\pi}{2^n}\right)}$$ 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.

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Leon D. Fairbanks. 2025-02-21. Sums of Powers of Sine and Generalized Bernoulli Polynomials. https://arxiv.org/abs/2502.15966

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