I want to integrate the following function with respect to x,between 0 and +Infinity:
-1/Pi Exp[-2 Pi x] Abs[w^3] (Abs[w])^(-x) Gamma[1 - x] Gamma[x - 3] (Sin[Pi x/2])^2 Cos[Pi x/2]
w is a parameter that ranges from - Infinity to Infinity, but you can set it to 2 if you want. As you can see, it has oscillatory factors and apparent singularities( since the Gamma function diverges but the Sin is zero, and the overall result is finite) at the positive integers.
As I try to integrate, i get the error
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in x near {x} = {0.996132}. NIntegrate obtained 0.008228086311816908
and 7.945116181892624
*^-6 for the integral and error estimates.
I have tried setting Method -> "LevinRule", setting workprecision to higher values, but nothing worked.... any ideas?