A [[Function]] $f: D \to \hat\C$ from some [[Domain]] $D\subseteq \hat \C$ onto the [[Riemann Sphere]] is considered holomorphic if it is [[Complex Numbers|Complex]] [[Derivative|Differentiable]] at all points in $D$. [[Complex Numbers|Complex]] Differentiability, symbolically, is the same as real differentiability - however this assertion is much stronger. $\huge f'(z)=\lim_{ s \to 0 } \frac{f(z+s) -f(z)}{z-s} $