if i substitue infinity instead of a"" into the formal formula
i get infinity
am i correct?
The best way to find the residue at infinity is to replace "z" by "1/z" and find the residue at z=0.
Here, " " is a constant so replacing z by 1/z gives which has a pole of order 3 at z=0. That has residue 0 at z= 0 so the residue of at infinity is also 0.
i am sorry i wrote the function in a wrong way
its
so by folowing your method
so the third derivative of sine is -cos z
and divide by 3!
and put 0 instead of z
and in the end i get
-1/6
correct?
Note that has a double pole at z = 0.
But in fact it's trivial to get the residue just by writing out the first few terms of the Laurent series around z = 0. Then it's crystal clear that the residue is .....