Question

f(z)= sinz/z^4
the laurent series is 1/z^3 -1/3!z+z/5!
my book says the Res(f,0)=the coefficient of z^-1=-1/6.
How was the Res(f,0) calculated?
In other words...how does one find z^-1 and hence its coefficient?

Answer 1

-1/3!z^3/z^4 = -1/6 (z^(-1)) <-- this is your residue

Answer 2

the left hand side of your expression isnt making sense to me

Answer 3

what is the coefficient of 1/z ??

Answer 4

-1/3!

Answer 5

ahh i see

Answer 6

hence -1/6 is the residue

Answer 7

yes

Answer 8

thanks