(11/07/2009, 07:06 AM)andydude Wrote:(11/05/2009, 03:48 PM)Gottfried Wrote: > >"A zero of order zero is a regular point at which theIs that the same as a pole of order zero? Hahaha

> >function is not zero."

It is kinda opposite. You get the order of a zero at a by dividing by (z-a)^m.

It is the maximum m such that f(z)/(z-a)^m is still holomorphic at a.

In the powerseries development it is the index of the first non-zero term,

e.g. f(z) = f_m (z-a)^m + f_{m+1)(z-a)^{m+1} + ....

So f(z)/(z-a)^m can not be 0 at a.