Monogenic Function

If

is the same for all paths in the complex plane, then  is said to be monogenic at . 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.

REFERENCES:

Newman, J. R. The World of Mathematics, Vol. 3. New York: Dover, p. 2003, 2000.