[math-fun] Do this one, Mascheroni, and you can stick the feather back in your cap.

Out[1028]= Sum[((-1)^n*QPolyGamma[0, -(Log[-(n/2)]/Log[2]), 1/2])/ n, {n, 1, Infinity}] == (-1 + EulerGamma - Log[2])*Log[2] In[1029]:= N@% Out[1029]= True