besselarray bug, was: Bessel plotting problem



For x>0 and real v

realpart(bessel_j(v,-x))=bessel_j(v,x)*cos(v*%pi)
imagpart(bessel_j(v,-x))=bessel_j(v,x)*sin(v*%pi)

I can use this.



 ------------Original Message------------
From: "Richard Hennessy"<rvh2007 at comcast.net>
To: "Robert Dodier" <robert.dodier at gmail.com>
Cc: "Maxima List" <maxima at math.utexas.edu>
Date: Fri, Jun-13-2008 7:51 PM
Subject: Re: [Maxima] besselarray bug, was: Bessel plotting problem

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

_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima