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: Simon & Schuster, p. 2003, 1956.

© 1996-9

1999-05-26