It has now been proven that there exists a unique function which is a solution of the equation and satisfies the additional conditions that and approaches the fixed points of the logarithm (roughly ) as approaches and that is holomorphic in the whole complex -plane, except the part of the real axis at . This proof confirms a previous conjecture. The construction of such a function was originally demonstrated by Kneser in 1950. The complex map of this function is shown in the figure at right. The proof also works for other bases besides "e", as long as the base is bigger than formula_99. Subsequent work extended the construction to all complex bases. The complex double precision approximation of this function is available online.