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MathGroup Archive 2002

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BesselZeros and Working Precision?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33841] BesselZeros and Working Precision?
  • From: aes <siegman at stanford.edu>
  • Date: Fri, 19 Apr 2002 02:29:00 -0400 (EDT)
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at wolfram.com

I'm puzzled by why the four alternative forms

      BesselJZeros[0,  1][[1]]

      N[ BesselJZeros[0,  1][[1]], 12]

      BesselJZeros[0,  1,  WorkingPrecision ->12][[1]]

      N[ BesselJZeros[0, 1, WorkingPrecision ->12][[1]], 12]

all give the same 6-digit answer, namely 2.40483, whereas

      BesselJZeros[0, 1, WorkingPrecision -> 30][[1]]

gives the 30-digit answer 

   2.4048255576957727686216318793264541313535027

I'm also *really* puzzled by why

      BesselJZeros[0, 1, WorkingPrecision -> 6][[1]]

 gives the *one*-digit answer "0".

This last one really seems like a bug; it's certainly a "gotcha".  I'm not 
arguing that there's any good reason for coding something with a reduced 
MachinePrecision like this -- but nonetheless I don't think it should give that 
answer!

Actually, here's a table of  BesselJZeros[0, 1, WorkingPrecision -> k][[1]] for 
k from 1 to 30.  Note erroneous answers at k = 7 and 8 also.

        {"1", "0"},
        {"2", "0"},
        {"3", "0"},
        {"4", "0"},
        {"5", "0"},
        {"6", "0"},
        {"7", "2.398095666212098`"},
        {"8", "2.404944945798332`"},
        {"9", "2.404825723910026`"},
        {"10", "2.404825723910026`"},
        {"11", "2.404825723910026`"},
        {"12", "2.404825723910026`"},
        {"13", "2.404825723910026`"},
        {"14", "2.4048255576957467`"},
        {"15", "2.4048255576957467`"},
        {"16", "2.4048255576957467`"},
        {"17", "2.4048255576957467`"},
        {"18", "2.4048255576957467`"},
        {"19", "2.4048255576957467`"},
        {"20", "2.404825557695772768622813251300758`20"},
        {"21", "2.404825557695772768622529251832104`21"},
        {"22", "2.404825557695772768622529251842381`22"},
        {"23", "2.404825557695772768622530855769674`23"},
        {"24", "2.404825557695772768622530855769332`24"},
        {"25", "2.40482555769577276862253084774527500835`25"},
        {"26", "2.40482555769577276862253084774527504299`26"},
        {"27", "2.40482555769577276862253084778108108087`27"},
        {"28", "2.40482555769577276862163187932659770515`28"},
        {"29", "2.4048255576957727686216318793265975336787736`29"},
        {"30", "2.4048255576957727686216318793264541313535027`30"}}


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