  The tacnode Riemann-Hilbert problem is a 4 x 4 matrix valued RH problem that
appears in the description of the local behavior of two touching groups of
non-intersecting Brownian motions. The same RH problem was also found by Duits
and Geudens to describe a new critical regime in the two-matrix model.
  Delvaux gave integral representations for some of the entries of the 4 x 4
matrix. We complement this work by presenting integral representations for all
of the entries. As a consequence we give an explicit formula for the
Duits-Geudens critical kernel.
