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"}}