# [Maxima] Bessel function with imaginary argument

Richard Hennessy rich.hennessy at verizon.net
Tue Jan 27 16:52:11 CST 2009

```Try this.

realpart(bessel_j(1,1*%i)),numer;
imagpart(bessel_j(1,1*%i)),numer;

the numer flag tells Maxima to give the answer in floating point.

The result you are getting symbolically is the exact answer which is, in the simplified form, itself.

Rich

----- Original Message -----
From: "Schirmacher, Rolf" <Rolf.Schirmacher at MuellerBBM.de>
To: <maxima at math.utexas.edu>
Sent: Tuesday, January 27, 2009 4:41 PM
Subject: [Maxima] Bessel function with imaginary argument

Hello,

I get the following strange result for bessel_j(1,z) with purely imaginary
argument:

First, try numerical evaluation:

(%i127) bessel_j(1,1.0*%i);
(%o127) 0.56515910399249*%i
(%i128) realpart(bessel_j(1,1.0*%i));
(%o128) 0
(%i130) imagpart(bessel_j(1,1.0*%i));
(%o130) 0.56515910399249

This looks fine. Now, if I want to get the realpart / imagpart symbolically,
it is wired:

(%i131) realpart(bessel_j(1,1*%i));
(%o131) bessel_j(1,%i)
(%i132) imagpart(bessel_j(1,1*%i));
(%o132) 0

What am I doing wrong?

I am using the pre-built Windows release:

wxMaxima 0.8.1 http://wxmaxima.sourceforge.net
Maxima 5.17.1 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (aka GCL)
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.

I am not an expert to maxima neither to lisp ...

Any hint is highly appreciated.

Thanks,

Rolf
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