  Notions of a "holomorphic" function theory for functions of a
split-quaternionic variable have been of recent interest. We describe two found
in the literature and show that one notion encompasses a small class of
functions, while the other gives a richer collection. In the second instance,
we describe a simple subclass of functions and give two examples of an analogue
of the Cauchy-Kowalewski extension in this context.
