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MathGroup Archive 1998

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BesselJZeros strangeness


  • To: mathgroup@smc.vnet.net
  • Subject: [mg12022] BesselJZeros strangeness
  • From: "L. Dwynn Lafleur" <lafleur@usl.edu>
  • Date: Fri, 17 Apr 1998 03:40:57 -0400
  • Organization: University of Southwestern Louisiana

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.  Consider the following cells
cut-and-pasted from a notebook.

--------------------

(*  First two input cells are from Mathematica 3.0 help file describing
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  *) In[4]:= BesselJZeros[0, 2]
Out[4]= {2.40483,5.52008}
In[5]:= BesselJZeros[0, 3]
Out[5]= $Aborted
In[6]:= BesselJZeros[0, 6]
Out[6]= $Aborted
In[7]:= BesselJZeros[0, 7]
Out[7]= {2.40483,5.52008,8.65373,11.7915,14.9309,18.0711,21.2116}
In[8]:= BesselJZeros[0, 20]
Out[8]=
{2.40483,5.52008,8.65373,11.7915,14.9309,18.0711,21.2116,24.3525,27.4935,

30.6346,33.7758,36.9171,40.0584,43.1998,46.3412,49.4826,52.6241,55.7655,
  58.907,62.0485}

---------------------

Note that, contrary to what is suggested in the help file, BesselJZeros
cannot calculate the first 5 zeros unless an AccuracyGoal setting is
explicitly stated.  This particular resulty is strange since the
default options for BesselJZeros are {WorkingPrecision->16,
AccuracyGoal->Automatic}, and according to the Mathematica
documentation, the Automatic setting for AccuracyGoal sets it to 10
fewer digits than WorkingPrecision, i.e. 6.  However, AccuracyGoal->8
works while the default does not.

We also see that BesselJZeros can be called to calculate the first 2
zeros but not the first 3 zeros or the first 6 zeros.  However, it can
calculate the first 7 zeros and the first 20 zeros. 

Would someone more experienced with Mathematica than I please explain
this behavior?  Thanks.

Dwynn

-- 

==============================================
   L. Dwynn Lafleur
   Professor of Physics
   The University of Southwestern Louisiana
   Lafayette, Louisiana  (USA)
   lafleur@usl.edu   
==============================================



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