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MathGroup Archive 2002

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Re: List, FindRoot, Bessel

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33634] Re: [mg33628] List, FindRoot, Bessel
  • From: BobHanlon at aol.com
  • Date: Thu, 4 Apr 2002 19:39:51 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 4/3/02 6:36:56 PM, alimir3 at cti.ecp.fr writes:

>I'm trying to find the first n roots of an equation involving Bessel
>Functions and to create a List of them.
>
>The best thing I find so far is :
>n = 10;
>For[i = 0, i < n,
>  Print[FindRoot[- k BesselJ[1, k] + 30 BesselJ[0, k] == 0, {k,
>        2.32 + i Pi}]];
>  i++]
>
>And the result I get is :
>
>{k->3.2}
>{k->5.2}
>{k->8.3}
>....
>
>Does anyone know what {k->3.2} means ? And how I could get only the value
>3.2 instead of {k->3.2} in order to create a list?

?->

lhs -> rhs represents a rule that transforms lhs to rhs.

n=10;

zeroes = Table[
    k /. FindRoot[-k *BesselJ[1,k]+30 *BesselJ[0,k]==0,{k,
          2.32+i *Pi}], {i,0,n-1}]

{2.3261434267611816, 5.340984403080474, 8.377067491414179,
 
  11.422149230489381, 14.47479669212884, 17.53481087253842,
 
  20.6020432139118, 23.67619890998608, 26.756844792287815,
 
  29.8434609966363}

Plot[-k *BesselJ[1,k]+30 *BesselJ[0,k],
 
    {k,0,30}, ImageSize->400,
 
    PlotStyle -> RGBColor[0, 0, 1],
    Epilog -> {RGBColor[1,0,0],
 
        AbsolutePointSize[4],
 
        Point[{#,0}]& /@ zeroes}];


Bob Hanlon
Chantilly, VA  USA


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