Differential relations for the largest root distribution of complex   non-central Wishart matrices
  A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density function is derived (for m=2,3) or conjectured. 
Raimundas Vidunas and Akimichi Takemura
math.ST stat.TH