Raymond Toy wrote:
> So, both bessel_j(a,x) and bessel_j[a](x) are recognized and produce
> the same results?
Correct. I can't find any differences between the way Macsyma
evaluates bessel_j(a,x) and bessel_j[a](x). They both even TeX to
$$ J_{a}\left(x\right) $$.
Further, the Macsyma documentation says that the names jo(x), j1(x),
and jn(x,n) "are still supported, but their use is discouraged."
>Using this syntax, can I take the derivative wrt to a still? This is
>a well-defined operation.
Macsyma (circa 2.2) doesn't know the derivatives of the
Bessel functions with respect to the order. I don't think
it is possible to use gradef to define the derivative of
bessel_j[a](x) with respect to both a and x. Maybe this
matters, maybe it doesn't to you; Macsyma doesn't appear
to use gradef to differentiate the Bessel functions.
One more thing: I'm guessing that some versions of Macsyma
used Miller's algorithm for numerical evaluation of the Bessel
functions (see A&S). After evaluating J_n(x), for a float x,
an array bessel_j_array held the values of J_0(x), J_1(x), ...
J_n(x). I wasn't able to test this; my Macsyma doesn't
seem to do this.
Barton