Abstract. We evaluate the matrix elements Or^p, where 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 ₃F₂(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.

Print publication: Issue 18 (28 September 2009)
Received 2 July 2009, in final form 3 August 2009
Published 9 September 2009