Use contour integration to show that \[ \int _0^\infty \frac {x^\alpha }{(1+x)^2}\,dx=\frac {\pi \alpha }{\sin \pi \alpha } \] where \(0<\alpha <1\).
Question
Math 6420 • PDE
Fall 2005 • Question 6
Question
Fall 2005 • Question 6
Use contour integration to show that \[ \int _0^\infty \frac {x^\alpha }{(1+x)^2}\,dx=\frac {\pi \alpha }{\sin \pi \alpha } \] where \(0<\alpha <1\).