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Plana's Summation Formula for $\sum^\infty_{m=1,3,\ldots} m^{-2} \sin(m \alpha), m^{-3} \cos(m\alpha), m^{-2} A^m, m^{-3} A^m$

This is a preview. Log in through your library . Abstract The four series $$\sum^\infty_0 \sin(2k + 1)\alpha/(2k + 1)^2, \quad\sum^\infty_0 \cos(2k + 1)\alpha/(2k + 1 ...