Show that \[ \int_{\RR_{\geq 0}}{x^{-s} \over x+1} = {\pi \over \sin(\pi s)} .\]
Solution
Sketch: see here.
$\int_0^\infty\frac{x^{-s}}{x+1}\,dx=\frac{\pi}{\sin(\pi s)}$
P-YWMCT
- Area
- Complex Analysis
- Topics
- Complex Logarithm, Contour Integration, Integrals, Residues
- Status
- draft