Question

Write the laurent series re of (1-exp(z))/(1+exp(z))

Answer 1

Find the Laurent series for the given function about the indicated point. Also, give the residue of the function at the point.

z↦

1

e

z

−1

z↦1ez−1

The point is

z

0

=0

z0=0

(four terms of laurent series).

I have wrote

e

z

−1

ez−1

as

z+

z

2

/2!+

z

3

/3!

z+z2/2!+z3/3!

....

Now i don't know how to proceed with this further.

Please answer in detail I am very weak with this.

Thank you.