Names of Bessel functions (Re: half integer bessel)

>>>>> "Barton" == Barton Willis <willisb@unk.edu> writes:

[snip]

This is a continuation of a discussion Barton and I were having on the
names of the bessel functions.

The issue is what the names of the Bessel functions should be.

Currently, the Bessel J function (and similarly for Y, I, and K) can
be accessed as either bessel_j(arg, order) or bessel_j[order](arg).
If you use the former, it is rewritten to be the latter.  I think
bessel_j[order](arg) is used because maxima already supported
%j[n](x).

But I think it's bad that we have multiple ways of specifying this.
We need to get rid of one of these ways.

    Barton> I prefer bessel_j(order, arg) over bessel_j[order](arg).

Are you changing bessel_j argument order?  This might be a problem for
existing code since it's currently the other way.  But I too would
prefer bessel_j(order, arg) over bessel_j(arg, order).  I'm undecided
whether the official name is bessel_j(order, arg) or
bessel_j[order](arg).

What does Macsyma do?

    Barton> (a) Maxima's internal representation for subscripted
    Barton>     functions is semi-unpleasant.

Only a problem for implementers. :-)  But yes, it's somewhat of a pain
to handle.

    Barton> (b) I recall reading a warning (maybe in commercial
    Barton>     macsyma) that translation of subscripted functions
    Barton>     from Maxima to Lisp doesn't work or doesn't work well.
    Barton>     It may be best to discourage their use.

If so, then, yes, this is a problem.

    Barton> (c)  If we want the bessel function order to visually be a
    Barton>      subscript, we can do this with some messing around
    Barton>      with dimension; for example from orthopoly

I don't think we need to do this, but it is rather nice when
displaying the function.

    Barton> (d) orthopoly doesn't use subscripted functions for orders
    Barton>     (and I'm too lazy to support both methods)

I don't think this is a problem.

Ray