Expectation values in relativistic Coulomb problems

We evaluate the matrix elements < Or(p)>, where O = {1, beta, i alpha n beta} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions F-3(2) (1) for all suitable powers. Their connections with the Chebyshev and Hahn polynomials of a discrete variable are emphasized. As a result, we derive two sets of Pasternack-type matrix identities for these integrals, when p -> - p - 1 and p -> - p - 3, respectively. Some applications to the theory of hydrogenlike relativistic systems are reviewed.