residue at infinity of f(z)=z^3 * cos(1/z-2)

Dec 2009
28
0
Hello all of you;

Kindly I ask you to guide to solve this problem:

Find the residue at infinity of f(z)=z^3 * cos(1/z-2)

I have an idea but I don't know how to proceed,
First we do expansion for cos(1/z-2) and then multiply by z^3 we obtain
z^3-z^3/2(z-2)^2+z^3/24(z-2)^4+...

the residue of f at the essential singularity 2 is the coefficient of ( 1/z-2) but I don't know how to obtain that coefficient?? then the residue at infinity will be same as residue at 2 but with negative sign
please help me to get the result

Thank you in advance

Thank you in advance