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?)