  In Neri and Schneider (2012) we presented a method to recover the Maximum
Entropy Density (MED) inferred from prices of call and digital options on a set
of n strikes. To find the MED we need to numerically invert a one-dimensional
function for n values and a Newton-Raphson method is suggested. In this note we
revisit this inversion problem and show that it can be rewritten in terms of
the Langevin function for which numerical approximations of its inverse are
known. The approach is very similar to that of Buchen and Kelly (BK) with the
difference that BK only requires call option prices. Then, in continuation of
our first paper, we presented another approach which uses call prices only and
recovers the same density as BK with a few advantages, notably, numerical
stability. This second paper provides a detailed analysis of convergence and,
in particular, gives various estimates of how far (in different senses) the
iterative algorithm is from the solution. These estimates rely on a constant m
> 0. The larger m is the better the estimates will be. A concrete value of m is
suggested in the second paper, and this note provides a sharper value.
