> Following mpmath conventions is a good idea, and I like airyai better
> anyway.

Ok. This is consistent with the Fresnels where we removed the "_" too.

> Regardless of what we do, I think we should use the notation
> that puts the derivative as one of the arguments rather than have a
> separate airy_prime function.

I vote against this for mainly two reasons:

- All formula become more complicated to read and write
  and we make the Airy function essentially a 2-Argument
  function.

- All other major CAS do provide separate functions
  which are also standard mathemtical notation.
  (Hence users may expect these functions. For example
  I overlooked the implementation of mpmath ;-))

Maybe there are even more reasons to do this, but these
two come to my mind right now.

You are right, for mathematical reasons we would not need
extra functions. We even could write an unevaluated derivative.
(Which in turn gives problems to express the second derivative
which should simplify to Airys again.) For the same reasons
we could express cos by sin or right away by exp.

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