Analytic Functions

A function is said to be analytic at iff it is differentiable throughout a neighbourhood of . Aka. regular functions, holomorphic functions and monogenic functions.

Examples

• Polynomial functions of (analytic everywhere)
• Functions with a converging Taylor series for all (analytic everywhere)

Non-examples

Function	Note
	Differentiable only at .
	Nowhere differentiable. Derivative taken on the real and imaginary axes are different.
	Similar to above.
	Similar to above.
	Similar to above.
	Similar to above.

Analytic implies differentiable