While performing the following (presumably) correct manipulations in Mathematica, I obtain a result that is missing a sign function. Is there a mistake in my code, or is there some bug in Mathematica? Let’s say we want to reproduce the following Fourier transform in Mathematica: $ $ \frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty dx \frac{e^{iwx}}{\sin(\pi x)}=\frac{i}{\sqrt{2\pi}}\text{sign}(w)\sum_{n=-\infty}^{\infty}e^{i n(\pi+w)}$ $ The FourierTransformRead more