  The slice Dirac operator over octonions is a slice counterpart of the Dirac
operator over quaternions. It involves a new theory of stem functions, which is
the extension from the commutative $ O(1) $ case to the non-commutative $ O(3)
$ case. For functions in the kernel of the slice Dirac operator over octonions,
we establish the representation formula, the Cauchy integral formula (and, more
in general, the Cauchy-Pompeiu formula), and the Taylor as well as the Laurent
series expansion formulas.
