  We review some recent results on recursion relations which help evaluating
arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\lambda$ and of
$\beta r^\lambda$ ($\beta$ a Dirac matrix) derived in the context of Dirac
relativistic quantum mechanics. Similar recursion relations were derived some
years ago by Blanchard in the non relativistic limit. Our approach is based on
a generalization of the second hypervirial method previously employed in the
non-relativistic Schr\"odinger case. An extension of the relations to the case
of two potentials in the so-called unshifted case, but using an arbitrary
radial function instead of a power one, is also given. Several important
results are obtained as special instances of our recurrence relations, such as
a generalization to the relativistic case of the Pasternack-Sternheimer rule.
Our results are useful in any atomic or molecular calculation which take into
account relativistic corrections.
