  We determine exact recurrence relations which help in the evaluation of
matrix elements of powers of the radial coordinate between Dirac relativistic
hydrogenic eigenstates. The power $\lambda$ can be any complex number as long
as the corresponding term vanishes faster than $r^{-1}$ as $r \to \infty$.
These formulas allow determining recursively any matrix element of radial
powers --$r^\lambda$ or $\beta r^\lambda$, $\beta$ is a Dirac matrix-- in terms
of the two previous consecutive elements. The results are useful in
relativistic atomic calculations.
