Monogenic function

A monogenic function is a complex function with a finite derivative. More precisely, a function $f(z)$ defined on $A\subseteq \mathbb {C}$ is called monogenic at $\zeta \in A$, if $f'(\zeta )$ exists and is finite, with:

$f'(z)=\lim _{z\to \zeta }{\frac {f(z)-f(\zeta )}{z-\zeta }}$

A function $f(x)$ which is monogenic $\forall \zeta \in B$, is said to be monogenic on $B$, and if $B$ is a domain of $\mathbb {C}$, then it is analytic as well. However if B is not a domain, but is sufficiently "massive", $f(x)$ possess a weakened form of analyticity