Manipulation of an analytic function

[thayin]

Can anyone point out a way to get f(z) = z + e^h(z) into the form f(z) = (1-e^(z*h(z)))/z

I have used all of the algebra tricks I know and it seems to be going nowhere.

 

[jackmell]

Did you try plugging in a number say z=1 to make sure they're equivalent?

 

[thayin]

I know they are equivalent. I am trying to understand a result not come up with a new one.

 

[Office_Shredder]

Is h(z) a specific function that you haven't mentioned? Because this is not true in general. For example if h(z)=z we get
$$z+e^z=\frac{1-e^{z^2}}{z}$$
Plugging in z=1 we get
$$1+e=1-e$$
which seems unlikely