About: Monogenic function

A monogenic function is a complex function with a single finite derivative. More precisely, a function defined on is called monogenic at , if exists and is finite, with: Alternatively, it can be defined as the above limit having the same value for all paths. Functions can either have a single derivative (monogenic) or infinitely many derivatives (polygenic), with no intermediate cases. Furthermore, a function which is monogenic , is said to be monogenic on , and if is a domain of , then it is analytic as well (The notion of domains can also be generalized in a manner such that functions which are monogenic over non-connected subsets of , can show a weakened form of analyticity)