[Maxima] Bessel plotting problem

Dieter Kaiser drdieterkaiser at web.de
Tue Jun 10 17:02:27 CDT 2008

```The Bessel functions are defined for all real and complex numbers of the order
and the argument. That's not the problem. But Maxima has limitations. The NEW
CVS Bessel code gives numerical values for all negative and positive orders and
real or complex arguments. The evaluation for complex order is still missing.

The error of the slatec routines below you can generated with the OLD Bessel
code.

Dieter Kaiser

-----Ursprüngliche Nachricht-----
Von: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] Im
Auftrag von Richard Hennessy
Gesendet: Dienstag, 10. Juni 2008 23:37
An: fateman at cs.berkeley.edu
Cc: Maxima List
Betreff: Re: [Maxima] Bessel plotting problem

I am going to take my conclusion back.  Just because Maxima gives an error
message while plotting does not mean the function is only defined for positive
x.

Learn, live.

R

------------Original Message------------
From: "Richard Hennessy"<rvh2007 at comcast.net>
To: fateman at cs.berkeley.edu
Date: Sat, Jun-7-2008 11:03 AM
Subject: RE: [Maxima] Bessel plotting problem

I think I made a mistake.  What I wanted to plot was the real valued function
(f+g+conjugate(f+g))/2 where f and g are linearly independent (complex)
solutions to my differential eq.  I tried using realpart() but that did not
work.  I should have tried the following.

plot2d(-(sqrt(3)/2-%i/2)*%i*'(bessel_y(1/6,-x^3/3))+'(bessel_j(1/6,-x^3/3))*sqrt
(x),[x,-20,.001], plot_format,gnuplot]), orthopoly_returns_intervals : false;

That worked.

The domain of the bessel_j or bessel_y function must be positive x only since
when I try

plot2d(-(sqrt(3)/2-%i/2)*%i*'(bessel_y(1/6,-x^3/3))+'(bessel_j(1/6,-x^3/3))*sqrt
(x),[x,-15,15],[plot_format,gnuplot]), orthopoly_returns_intervals : false;

I get
-->

***MESSAGE FROM ROUTINE DBESY IN LIBRARY SLATEC. ***POTENTIALLY RECOVERABLE
ERROR, PROG ABORTED, TRACEBACK REQUESTED *  X LESS THAN OR EQUAL TO ZERO *
ERROR NUMBER = 2 *    ***END OF MESSAGE  ***JOB ABORT DUE TO UNRECOVERED ERROR.0
ERROR MESSAGE SUMMARY LIBRARY    SUBROUTINE MESSAGE START             NERR
LEVEL     COUNT SLATEC     DBESY      X LESS THAN OR EQUAL         2         1
1

When x is positive, the plot shows only the second and third quadrants with
actual points.  I think the first a fourth are not in the domain since I get
this ugly error message when it is done.

I would call this a bug, I am not sure if it is.  Is there a reason for the
restriction x > 0?

Rich

------------Original Message------------
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: "'Richard Hennessy'" <rvh2007 at comcast.net>
Date: Sat, Jun-7-2008 10:11 AM
Subject: RE: [Maxima] Bessel plotting problem

I haven't tried it, but how about removing the '  and
doing plot2d(  realpart( ....)..)

or plot2d ('(realpart( ...) ..))..
RJF

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