Residue Calc: (z^2 e^z)/(1+e^2z)

[hokhani]

what is the residues in below function?

(z^2 e^z)/(1+e^2z )

 

[SVXX]

Kindly show us your working first!
And if I were you, I'd follow these steps -:

1. Check the function where it ceases to be analytic, a point which is called a pole. In this case it is e^2z = -1 (Why?).
2. Expand the denominator (probably twice) to check the principal part of the Laurent expansion as to what order the pole(e^2z = -1) might be.
3. Find the residue at the pole using known methods.

 

[hokhani]

ok
thanks
but e^2z=-1 has many reply that they are:
z=i(2n+1)pi/2
I must calculate all the residues(in this case is infinite!)?

 

[SVXX]

What is the exact question?

 

[hokhani]

It sounds I got it
for
e^2z = -1
we have:
z=i(2n+1)pi/2 ;n=0,1,2,3,......
between[0,2pi] there are just two points:
z=i(pi/2) & i(3pi/2)
and we have to find the residues at these points.

please let me know if it is true or not.

 

[SVXX]

Okay yes, in [0, 2pi] those are the only points you have. Go ahead and calculate the residues at those points, for a simple pole e^2z = -1.