Monogenic Function

If

$$\lim_{z\to z_0} {f(z)-f(z_0)\over z-z_0}$$

is the same for all paths in the Complex Plane, then $f(z)$ is said to be monogenic at $z_0$. Monogenic therefore essentially means having a single Derivative at a point. Functions are either monogenic or have infinitely many Derivatives (in which case they are called Polygenic); intermediate cases are not possible.

See also Polygenic Function

References

Newman, J. R. The World of Mathematics, Vol. 3. New York: Simon & Schuster, p. 2003, 1956.