Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of   Hadjicostas's Formula
  We give analogs for Euler's constant and ln(4/Pi) of the well-known double integrals for zeta(2) and zeta(3). We also give a series for ln(4/Pi) which reveals it to be an "alternating Euler constant." 
Jonathan Sondow