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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