aiming at such accuracy for $p(f)$.

The probability distribution given in Eq. (\[eq:pf1\]) and (\[eq:pf2\]) cannot be normalized and the first moment $\langle f\rangle$ is also divergent. We shall compute the latter separately in the next section.\
An analytic continuation of the generating function for the moments of $f$ can be obtained from Eq. (\[eq:pf1\]) and (\[eq:pf2\]) by a direct calculation. We get e\^[f]{} = 2CC\_1 { -(-)+()+ }, \[eq:moments\] keeping in mind that this formula can be used only for moments of second order or higher.

The analytical structure of Eq. (\[eq:moments\]) is particularly simple. There are poles on the positive real $\nu$-axis, fully contained in the first term $-\nu\psi(-\nu)$: They correspond to positive values of $f$. All the other poles, contained in the remaining terms, are located on the real negative axis, and correspond to negative values of $f$.\
A comment is in order on the conjectured probability distribution (\[eq:proba\]) of the tip fluctuations that we used in the above derivation. Actually, we omitted a time-dependent Gaussian factor of the form $e^{-\delta^2/(4t_1)}$, which would cut off the exponential distribution of $\delta$ at a distance $2\sqrt{t_1}$ ahead of the tip of the front, and thus modify the distribution of 