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MathGroup Archive 2001

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Re: Bessel Function Zeros at 0 Not Given?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31816] Re: Bessel Function Zeros at 0 Not Given?
  • From: aes <siegman at stanford.edu>
  • Date: Mon, 3 Dec 2001 01:45:07 -0500 (EST)
  • Organization: Stanford University
  • References: <9ua3l3$190$1@smc.vnet.net> <9ucst9$dr7$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

> On Sat, 1 Dec 2001 08:16:35 +0000 (UTC), in comp.soft-sys.math.mathematica 
> I wrote:
> 
> >Isn't BesselJ[1,x] considered to have a zero at x = 0?  Seems odd that 
> >BesselJZeros[1,5] doesn't give it.
> >
> >At a minimum, the Standard Package documentation might mention this, to 
> >alert the user . . .


In article <9ucst9$dr7$1 at smc.vnet.net>, Tom Burton <tburton at cts.com> then wrote:

> The second paragraph of the Help includes the phrase "positive zeros". I 
> consider myself properly warned.


Well, just to be picky on this, on my machine anyway, when I type "BesselJZeros"    
into a notebook, hit the Help button, then click on the 
"NumericalMath`BesselZeros" link that appears, the primary thing that appears in 
the Help window is a pink shaded box containing about 8 examples, each of the 
form

   BesselJZeros[n \nu, n]     give a list of the first n zeros of J_\nu(x)

There are 3 lines of text visible above this box.  Hidden above this, not seen 
unless you scroll up, is a sample formula which is a solution of the heat 
equation in an expansion in the zeros of J0, which of course has no zero at x=0.

Nowhere in the entire section that I can see -- though my eyesight has 
admittedly deteriorated with advancing years -- does it say "gives a list of the 
first n *positive* zeros".

(Incidentally, is the "n \nu" in the 8 examples a misprint?)


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