Let $z$ be a complex number and let $f(z)$ be any transcendental entire function.
Is it true that $f(z) = C + \exp a + \exp b + \exp c $ where $ a,b,c $ are entire functions of $z$ and $C$ is a constant ?
If so, for a given $f$ in Taylor form is there an easy way to compute $a,b,c,C$ ?
Note that $C$ is not neccessarily equal to $f(0)$.
If the conjecture is true is there a unique solution for every $f(z)$ ?