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control-c and modified Bessel function bugs

  • To: mathgroup
  • Subject: control-c and modified Bessel function bugs
  • From: perry at pacific.mps.ohio-state.EDU
  • Date: Mon, 20 Mar 89 14:57:06 CST

I wanted to report two bugs I've found in version 1.1 of Mathematica running on
a SUN 4/110.  During runaway calculations, if I use ^C and then try to abort
my calculation, my SUN crashes with a "watchdog reset" message. It is possible
that this problem is related to our local configuration of SUN's.

The second bug also exists in the Mac version of Mathematica. Try:

In[1]:= Plot[BesselK[1/2,x],{x,20,25}]

The resultant output looks like noise.  The problem exists for other values of
l, but I have not thoroughly tested other special functions.  The problem does
not seem to occur outside of a special region, making me suspect that a poor
marriage between different numerical algorithms has been made. I'm probably
naive, but it would seem worthwhile for Wolfram Research to compile a series of
tests which use tabulated results from Abromowitz and Stegun and other sources. 

Some things Mathematica can't do that I would like to see:

Limit[eps Gamma[eps],eps -> 0]

Limit[E^(-.2 x+1),x -> Infinity]  for Integrate[E^(1-0.2x),{x,0,Infinity}]

Integrate[x/(a+b x^2+c x^4),x]    --macsyma will do this

Integrate[x^2/(a+b x^2+c x^4),x]  -Gradshteyn & Ryzhik 2.161

Integrate[1/x^3/(a+b x)^(1/3),x]  -G&R 2.236

Integrate[1/Sqrt[a+b E^(m x)],x]  -G&R 2.315

Integrate[Sinh[a x+b] Sinh[c x+d],x]    G&R 2.425

Integrate[Sinh[a x] Sinh[b x] Cosh[c x],x]   G&R 2.426

Macsyma will do most of the above, but it is usually slower than
Mathematica.  There are many times when I want to find a Series about
Infinity, but am forced to introduce 1 over the original variable and
take a series about zero instead.

It is extremely unfortunate that the SUN version of Mathematica does not
contain a NOTEBOOK facility.  This cripples Mathematica to some extent.
It would also be great if the graphics windows on the SUN had some
walking menus that allowed the user to alter options, instead of having
to use Show.  How about using the mouse to set light sources and rotate
surfaces?  CPU speed isn't there yet, but I can dream.

Having finished bitching, let me say I love this program.  It's good
enough that it's constantly got me thinking about what the "perfect"
package would be.

Robert Perry
Dept. of Physics
The Ohio State University
perry at
bitnet: perry at ohstpy

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