Sums of Powers of Sine and Generalized Bernoulli Polynomials

Leon D. Fairbanks

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…