3. As stated earlier, we have spherical harmonic functions (with much scope for dev) we are yet to have elliptical and cylindrical harmonic function, which may be developed.
This sounds very doable. How much work do you think would be involved?
As Stefan so rightly pointed out, the function for spherical
harmonic function, sph_harm at present calls lpmn thus evaluating all
orders <N. An initial glance at the code and the algorithm gives me a
feeling that it would be very well possible to avoid that by maybe
avoiding the dependence on lpmn.
Further, we can introduce ellipsoidal harmonic functions of first
kind and the second kind. I am confident about about the implementation
of ellipsoidal H function of first kind but don't know much about the
second kind. But I believe we can work it out in due course.And
cylindrical harmonics can be carried out using Bessel functions.