- #1
elimenohpee
- 67
- 0
Homework Statement
I need to calculate the residue of a function at infinity. My teacher does this by expanding the function in a laurent expansion and deduces the value from that. That seems much harder than it needs to be. For example, in the notes he calculates the residue at infinity of:
[tex]g(z)=\frac{\sqrt{z^{2}-1}}{z-t}=...=-t[/tex]
Is there an easier way than resorting to a laurent series? If I let z approach infinity in the function above, I get 1 not -t, so I'm assuming you can't evaluate the residue in that way?
Specifically I need to find the residue at infinity of
[tex]f(z)=\frac{z^{2}}{\sqrt{z^{2}-1}(z-t)}[/tex]
but I'm looking for a method to do so.