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Contour Illuminates

Posted: Sun Jul 10, 2016 11:02 am
by Tolaso J Kos
Show that:
$$\int_{-\infty}^{\infty}\cos \left ( ax^2 \right )\frac{\sinh\left ( 2ax \right )}{\sinh \left ( \pi x \right )}\,dx =\sin a, \; \left | a \right |\leq \frac{\pi}{2}$$