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Computation of Integral [entire topic moved to new forum]

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\[ \displaystyle \int_{- \infty}^{+ \infty} {e}^{-2 \pi i x \xi} \frac{ \sin \pi \alpha }{ \cosh \pi x  + \cos \pi \alpha } \mathrm{d} x = 2 \frac{ \sinh 2 \pi \alpha \xi }{ \sinh 2 \pi \xi } \]

where \( \displaystyle \xi \in \mathbb{R} \, , \, \alpha \in \left(0,1\right) \).

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