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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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