  Based on the multivariate saddle point method we study the asymptotic
behavior of the characteristic polynomials associated to Wishart type random
matrices that are formed as products consisting of independent standard complex
Gaussian and a truncated Haar distributed unitary random matrix. These
polynomials form a general class of hypergeometric functions of type \(_2
F_r\). We describe the oscillatory behavior on the asymptotic interval of zeros
by means of formulae of Plancherel-Rotach type and subsequently use it to
obtain the limiting distribution of the suitably rescaled zeros. Moreover, we
show that the asymptotic zero distribution lies in the class of Raney
distributions and by introducing appropriate coordinates elementary and
explicit characterizations are derived for the densities as well as for the
distribution functions.
