While adding the numeric routines for the bessel functions, it
occurred to me that what maxima has is somewhat messy. There's j0(x),
j1(x), and jn(x, n) which compute the Bessel functions for order 0, 1,
and integral n for real x. Then there's bessel(z,a) which computes
the Bessel function for complex z, and real order a.
I propose that we deprecate these names and use bessel_j(z,a) as the
main routine for all of these. (What does macsyma call this function?
Maybe we should use the same name as macsyma.)
I think this change is safe since the old names are still available,
and the new name isn't used by maxima code.
Similar arguments follow for i0, i1, in, with the name besseli.
Oddly, there's no implementation of y0, y1, etc. Slatec has routines
for these as well, so I'll add them with the name bessely.
There's also g0, g1, gn which I think is the exponentially-scaled
I(x,a). Not sure what to call this---maybe an optional parameter to
besseli?
I also note that maxima doesn't know any of the mathmetical properties
of Bessel functions. A bug.
Ray