Hi all

I'm trying to get my head around the Laurent series for the following function :

f(z) = zsinh(1/z+1)

about -1 and trying to give the general term of the series for odd and even powers of (z+1).

Also, how would I write down a punctured open disk D, containing the circle C={z:|z+1|=1} of which f is represented on this series, and what would be the nature of teh singularity of f at -1.

Any help would be greatly appreciated.

Many thanks