  Motivated by recent results in random matrix theory we will study the
distributions arising from products of complex Gaussian random matrices and
truncations of Haar distributed unitary matrices. We introduce an appropriately
general class of measures and characterize them by their moments essentially
given by specific Jacobi polynomials with varying parameters. Solving this
moment problem requires a study of the Riemann surfaces associated to a class
of algebraic equations. The connection to random matrix theory is then
established using methods from free probability.
