Dear All

The z is the complex variable and the function f(z) is defined as (exp(z^2)-1)/(z^2) if z not equal zero and defined as 1 if z=0 . It is asked for its differentiation up to 2k steps evaluated at z=0 i.e. f(2k)(0) . The answers are as :

1) 2k(2k-1) .... (k+2)

2) (2k)!/(k)!

3) 1

4) not computable , since not analytic at z=0

Which one is correct in your opinion ?