There are just two small comments that can be addressed before the acceptance 
and without any need of further reviewing:

- First, please indicate in the caption of Fig. 3 that the z (color) scale is 
running between 0 and 2\pi/3 and/or, alternatively, use a scale ticks in the 
color bar which corresponds to fractions of pi (e.g. 0 - \pi/6 - \pi/3 - 
\pi/2 - 2\pi/3). This is a bit confusing now that the caption says "intensity", 
which implies a number between 0 and 1 and 2\pi/3 is pretty close to 2.

Response: Good suggestion.  For clarity we have now normalized this plot so that the
uneclipsed flux is unity, and have edited the caption to reflect this.

- Second, please use one of the notations found here: 
https://en.wikipedia.org/wiki/One-sided_limit in order to note the one-sided 
limit after Eq. 88 (middle of page 29).

Response:  We were inaccurate in using the word "limit".  What we meant
is to describe the range of k^2 for which the formulae are valid.   We have
corrected the wording.


In addition to these changes, we have added additional references in the
introduction for background reading on transiting exoplanets.  We have
also added a new subsection, 10.1, with two new figures, 12 & 13, which
discuss the limits of the precision of the code for high order limb-darkening.
We hope the additions will be useful to the readers of the paper and
users of the code.

 

