  Let $A$ be a right linear operator on a two-sided quaternionic Banach space
$X$. The paper studies the Drazin inverse for right linear operators on a
quaternionic Banach space. It is shown that if $A$ is Drazin invertible then
the Drazin inverse of $A$ is given by $f(A)$ where $f$ is $0$ in an axially
symmetric neighborhood of $0$ and $f(q) = q^{-1}$ in an axially symmetric
neighborhood of the nonzero spherical spectrum of $A$. Some results analogous
to the ones concerning the Drazin inverse of operators on complex Banach spaces
are proved in the quaternionic context.
