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 ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...