Hermitian Symmetric Spaces of Tube Type and Multivariate Meixner-Pollaczek Polynomials

Harmonic analysis on Hermitian symmetric spaces of tube type is a natural framework for introducing multivariate Meixner-Pollaczek polynomials. Their main properties are established in this setting: generating and determinantal formulae, difference equations. As an application we consider the problem of evaluating moments related to a multivariate Barnes type integral involving the Harish-Chandra $c$-function of a symmetric cone.