So we were given a problem and it follows some of the stuff we did with Picard's theorems in class, but we were never shown how to actually find the form, just what they looked like for a few cases like not equal to a constant, or not equal to z.
f(z) is entire and $f(z)\ne\frac{1}{z}$ for $z\ne0.$ We have to show that this can be rewritten as $\frac{1-e^{zh(z)}}{z}$ where h(z) is entire. I have no clue where to get started. I know we would use the fact the function is entire and you have a branch of the Log, but not sure how to use that in this case.