Source: /cirosantilli/holomorphic-function

= Holomorphic function
{wiki}

Being a complex holomorphic function is an extremely strong condition.

The existence of the first derivative implies the existence of all derivatives.

Another extremely strong consequence is the <identity theorem>.

"Holos" means "entire" in Greek, so maybe this is a reference to the fact that due to the identity theorem, knowing the function on a small open ball implies knowing the function everywhere.