*To*: mathgroup@smc.vnet.net*Subject*: [mg12058] Re: [mg12022] BesselJZeros strangeness*From*: David Withoff <withoff@wolfram.com>*Date*: Fri, 24 Apr 1998 01:52:28 -0400

> I am using Mathematica 3.0.1 in Windows 95. I obtain rather strange (at > least, to me) results when using the BesselJZeros function in the > NumericalMath`BesselZeros` package. > > In[1]:= << NumericalMath`BesselZeros` > > In[2]:= BesselJZeros[0, 5] > > Out[2]= $Aborted > > (* Above aborted after about 3 minutes of no output *) > > In[3]:= BesselJZeros[0, 5, AccuracyGoal->8] > > Out[3]= {2.40483,5.52008,8.65373,11.7915,14.9309} > > (* Above output appears in much less than one second *) > > Would someone more experienced with Mathematica than I please explain > this behavior? Thanks. This is a problem in machine-number evaluation of BesselJ in Mathematica Version 3.0.1 for Windows. I do not believe there are any other affected versions. I don't know if the problem is in Mathematica or in Windows, and I suppose it doesn't matter. The solution is to avoid machine numbers, or to otherwise adjust the way numerical errors work out in the calculation. For more information see the Wolfram Research web site (http://www.wolfram.com/ support/Kernel/Symbols/NumericalMath/BesselZeros/BesselJZeros.html). All of these examples will finish in a few seconds if you avoid machine numbers. Dave Withoff Wolfram Research