Subject: besselarray bug, was: Bessel plotting problem
From: Richard Hennessy
Date: Fri, 13 Jun 2008 19:51:53 -0400
Maybe I am just showing off but I think from empirically looking at the data for bessel_j for negative argument and positive fractional order that there really is a relationship for bessel_j(v, -x) = cos(n*%pi/something) * bessel_j(v, x) (or something similar). I don't know about bessel_y since I haven't looked at that yet.
Rich
------------Original Message------------
From: "Robert Dodier" <robert.dodier at gmail.com>
To: "Richard Hennessy" <rvh2007 at comcast.net>
Cc: "Maxima List" <maxima at math.utexas.edu>
Date: Mon, Jun-9-2008 9:54 PM
Subject: besselarray bug, was: Bessel plotting problem
On 6/7/08, Richard Hennessy <rvh2007 at comcast.net> wrote:
> plot2d(-(%i/2+sqrt(3)/2)*%i*'(bessel_y(1/6,-x^3/3))+(bessel_j(1/6,-x^3/3))*sqrt(x),[x,.001,2],[plot_format,gnuplot]),orthopoly_returns_intervals : false;
Richard, I suspect the origin of the plot problem is this:
bessel_y(1/6,-x^3/3), x=0.001, numer;
=> BESSEL-Y: symbol $BESSELARRAY has no value
Looking at src/bessel.lisp (line 486) in the 5.15.0 source code,
it looks like $BESSELARRAY is referenced before it is assigned
anything. But only if the second argument < 0. Can you use an
identity to change the bessel_y expression to something with
second argument > 0 ??
The $BESSELARRAY stuff was cut out entirely post-5.15.0.
So maybe you could try downloading the current version from CVS:
http://maxima.cvs.sourceforge.net/maxima/maxima/src/bessel.lisp
and load that into your Maxima session & try the plot again.
HTH
Robert Dodier