I know that in complex analysis there is holomorphic function and an anti-holomorphic function. The definitions of derivative for both functions are subtly different.
As a non-mathematician, I would like to know if there is a way to "analyze" complex functions which are neither holomorphic not anti-holomorphic? What are they known as?
For example the function z+(e^(z*)) is neither holomorphic nor anti-holomorphic, even though it has no singularities.