$$ \left (\frac {d^{a-1}}{dz^{a-1}} z^a +a^2\right) $$
I understand that this is a derivative with respect to z , and that if instead of $( {a-1}) $ this was 2 it would be the second derivative. But i have no idea what to do with the a-1 , any help would be much appreciated!
-- Both z and a are complex variables
See that if $a=3$, you have the 2nd derivative of $z^3$ which is $3\cdot 2z = 3!z$
If $a=4$, you have the 3rd derivative of $z^4$, which is $4\cdot 3\cdot 2z=4!z$
So a pattern emerges.
I'm assuming $a$ has to be a positive integer. (If not, then we're talking fractional derivatives and that's a HUGE can of worms.)