Timeline for What algorithm does (or did?) Excel use for Bessel functions that is discontinuous at x=8?
Current License: CC BY-SA 4.0
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| May 22, 2022 at 0:08 | answer | added | Rob Matson | timeline score: 4 | |
| Jun 15, 2020 at 12:00 | history | tweeted | twitter.com/StackSciComp/status/1272499127029506048 | ||
| Jun 15, 2020 at 9:28 | history | edited | uhoh | CC BY-SA 4.0 |
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| Oct 7, 2018 at 14:05 | comment | added | Chris H | @uhoh, luckily I can truthfully say that my knowledge is so outdated as to be of little use to anyone - which is good as I provide similar assistance for a lot of other software | |
| Oct 7, 2018 at 14:01 | comment | added | uhoh | @ChrisH I just saw this in a news feed, I don't subscribe but the title is funny wsj.com/articles/… | |
| Oct 2, 2018 at 14:53 | comment | added | Chris H |
@Kirill the jump is definitely where you thought: BESSELJ(7.99999952316284,3)=-0.291132200533783000 but BESSELJ(8.00000095367431,3)=-0.291125245492850000 forcing digits until they're all zero in excel 2013 for windows. The latter matches `BESSELJ(8,3) to 8 dp
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| Sep 28, 2018 at 18:22 | comment | added | uhoh | @Kirill Thanks, I'm struggling to coax digits out of Excel. At the bottom of the question I've added some numbers that I've had to hand copy/paste one at a time to reveal digits. I don't remember how to get more. At some point we may need the help of someone who knows how to use Excel. This is Excel for Mac 2011 and the help is quite awkward. signing off for the night... | |
| Sep 28, 2018 at 18:19 | history | edited | uhoh | CC BY-SA 4.0 |
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| Sep 28, 2018 at 18:02 | comment | added | Kirill | Out of curiosity, can you try 7.999999523162841796875 and 8.00000095367431640625 (printing the output to full precision), the two Float32 numbers next to 8? | |
| Sep 28, 2018 at 16:07 | history | edited | Anton Menshov♦ | CC BY-SA 4.0 |
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| Sep 28, 2018 at 11:04 | history | edited | uhoh | CC BY-SA 4.0 |
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| Sep 28, 2018 at 11:01 | comment | added | uhoh | @gammatester I'm quite rusty at excel now, but here is what I can do. I've just plotted change since 7.999997 as a rough check. Both even and odd but it stops at J9! (editing question) See i.sstatic.net/0YlZA.jpg and also i.sstatic.net/nFnzV.jpg Also, I don't see non integral orders available. | |
| Sep 28, 2018 at 10:39 | comment | added | Kirill | The starting point for me for computing special functions has always been the DLMF. According to that (dlmf.nist.gov/10.74#i), it could be a switch between a power series and an asymptotic expansion, but obviously that doesn't prove anything. | |
| Sep 28, 2018 at 10:18 | comment | added | gammatester | Without the actual implementation, you can only guess. My guess is, that the integer order Bessel functions are computed from $J_0, J_1$ with the recurrence relation. And (and least) in the $J_1$ implementation there is a switch between two approximations. (E.g. netlib.org/fdlibm has a switch at $x=8$). Do the even-order functions are 'discontinuous' too? Can you check with real order Bessel functions, e.g. $J_{3\pm0.00001}(8)?$ | |
| Sep 28, 2018 at 8:37 | history | edited | uhoh | CC BY-SA 4.0 |
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| Sep 28, 2018 at 8:05 | history | edited | uhoh | CC BY-SA 4.0 |
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| Sep 28, 2018 at 7:05 | history | edited | uhoh | CC BY-SA 4.0 |
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| Sep 28, 2018 at 6:36 | history | edited | uhoh | CC BY-SA 4.0 |
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| Sep 28, 2018 at 6:31 | history | asked | uhoh | CC BY-SA 4.0 |
