Names of Bessel functions (Re: half integer bessel)

>>>>> "Richard" == Richard Fateman <fateman@cs.berkeley.edu> writes:

    Richard> If you want functions to provide numbers, the usual route
    Richard> is notationally wasteful, with specific functions for
    Richard> Bessel functions of integer order and real argument.
    Richard> Then other functions for non-integer and/or complex order
    Richard> and argument would have different program names.

I didn't quite follow this.  What "usual route"?

    Richard> One piece of guidance in this is to return the favor of Mathematica, which
    Richard> did so much copying from other systems, including Macsyma, and use the
    Richard> same notation as in Mathematica.  BesselJ[n,x]   which in Macsyma syntax
    Richard> actually would be BesselJ(n,x)  since Mathematica uses [] for enclosing
    Richard> "function" arguments.

This is acceptable to me, but I would use bessel_j(n,x) instead of
BesselJ(n,x).  (I hate typing Mathematica function names.  Too many
shifted characters.)

Ray