Analyticity at Infinity

1. Jul 3, 2008

Palindrom

How does one define, given a complex function, the following:

• The function is analytic at infinity.
• The derivative of the function at infinity.

It turns out that it's supposed to be quite common to define these terms, however I have never been shown either of them. I have a few guesses, but along with some lecture notes I could put my hands on, it's all become a big mess for me.

2. Jul 3, 2008

matt grime

Presumably one replaces z with w=1/z and works w=0.

3. Jul 4, 2008

Palindrom

O.K., but then if g(z)=f(1/z) do I take f'(\infty)=g'(0)? Just like this?