# [Maxima] bessel_i quadpack bug 5.26.0

Edwin Woollett woollett at charter.net
Mon Feb 27 16:06:06 CST 2012

```With 5.26.0 gcl ( and in 5.25.1 gcl) I get
quadpack returning a noun form if integer
orders are used for the cases:

imagpart(bessel_i(odd,%i*x))
and:
realpart(bessel_i(even,%i*x))

To get a numerical answer, I need to
use float orders, as in

imagpart(bessel_i(1.0,%i*x))

This behavior makes it difficult to design a
bessel functions (ie., implementing "nintegrate").
----------------------------------------
(%o1) [qs]

(%i2) qs(imagpart(bessel_i(1,%i*x)),x,1,2);
(%o2) qs(-%i*bessel_i(1,%i*x),x,1,2,epsrel = 1.0E-8,epsabs = 0.0,limit =
200)

(%i3) qs(imagpart(bessel_i(1.0,%i*x)),x,1,2);
(%o3) [0.54130690741673,6.0097139200269267E-15,21,0]

(%i4) qs(realpart(bessel_i(2,%i*x)),x,1,2);
(%o4) qs(bessel_i(2,%i*x),x,1,2,epsrel = 1.0E-8,epsabs = 0.0,limit = 200)

(%i5) qs(realpart(bessel_i(2.0,%i*x)),x,1,2);
(%o5) [-0.23269143908339,2.5833939330353786E-15,21,0]

(%i6) qs(imagpart(bessel_i(3,%i*x)),x,1,2);
(%o6) qs(-%i*bessel_i(3,%i*x),x,1,2,epsrel = 1.0E-8,epsabs = 0.0,limit =
200)

(%i7) qs(imagpart(bessel_i(3.0,%i*x)),x,1,2);
(%o7) [-0.065445820049256,7.2659456284159177E-16,21,0]

(%i8) qs(realpart(bessel_i(4,%i*x)),x,1,2);
(%o8) qs(bessel_i(4,%i*x),x,1,2,epsrel = 1.0E-8,epsabs = 0.0,limit = 200)

(%i9) qs(realpart(bessel_i(4.0,%i*x)),x,1,2);
(%o9) [0.013931648099919,1.5467236491505718E-16,21,0]

(%i10) qs(imagpart(bessel_i(5,%i*x)),x,1,2);
(%o10) qs(-%i*bessel_i(5,%i*x),x,1,2,epsrel = 1.0E-8,epsabs = 0.0,limit =
200)

(%i11) qs(imagpart(bessel_i(5.0,%i*x)),x,1,2);
(%o11) [0.0024076583623394,2.6730377493005542E-17,21,0]

(%i12) qs(realpart(bessel_i(6,%i*x)),x,1,2);
(%o12) qs(bessel_i(6,%i*x),x,1,2,epsrel = 1.0E-8,epsabs = 0.0,limit = 200)

(%i13) qs(realpart(bessel_i(6.0,%i*x)),x,1,2);
(%o13) [-3.5190404859839462E-4,3.9069197721274786E-18,21,0]

(%i14) build_info()\$
Maxima version: 5.26.0
Maxima build date: 22:48 1/15/2012
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8
-------------------------------------------
Ted Woollett

```