Mathematical Jokes

[bo198214]

> >"A zero of order zero is a regular point at which the
> >function is not zero."

Is that the same as a pole of order zero? Hahaha

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.