Re: how to find roots of Bessel zero's
- To: mathgroup at smc.vnet.net
- Subject: [mg22796] Re: how to find roots of Bessel zero's
- From: "Richard I. Pelletier" <bitbucket at home.com>
- Date: Sat, 25 Mar 2000 03:58:35 -0500 (EST)
- References: <8bfe82$ibv@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <8bfe82$ibv at smc.vnet.net>, "Yury Logvin"
<yury at crosslight.com> wrote:
> Dear Mathematica's gurus!
>
> If I need find zero's of Bessel functions
> e.g. BesselJ0[x] = = 0
> ( numerical values of x, not analytical ones),
> can I do this with Mathematica
> using commands like Solve or Roots ?
>
I am far from a guru, but I _just_ happened to be doing a homework
problem last week that asked that very question. Mathematica isn't
happy using Solve to find zeroes of Bessel functions (although it
worked fine for Hermite, Legendre, and Laguerre polynomials!).
But if you look up Bessel in the general index, you will find a package
called BesselZeros, which has several functions in it for finding
zeroes, e.g. to find the first 5 zeroes of Bessel J0, enter
BesselJZeros[0.,5]
On the other hand, a technique someone else showed _me_, of greater
generality, is to use FindRoot after plotting the functions of interest
so you have approximate values for the zeroes:
to find the zero near 2, once you know there's one there:
FindRoot[BesselJ[0,x]\[Equal]0, {x,2}]
or, to find the 6 zeroes near {2,5,9,12,15,18} :
FindRoot[BesselJ[0,x]\[Equal]0, {x,#}]&/@{2,5,9,12,15,18}
Vale,
Rip
--
If we aren't supposed to eat animals, why are they made of meat?
Richard I. Pelletier
NB eddress: r i p 1 [at] h o m e [dot] c o m