Defining Analyticity at Infinity: How Do You Define and Calculate It?

[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.

 

[matt grime]

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

 

[Palindrom]

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