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MathGroup Archive 1998

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Re: roots of BesselJPrimes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14165] Re: [mg14152] roots of BesselJPrimes
  • From: BobHanlon at aol.com
  • Date: Wed, 30 Sep 1998 02:04:14 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Christian,

$Version

"Power Macintosh 3.0 (May 6, 1997)"

Needs["NumericalMath`BesselZeros`"]

BesselJPrimeZeros[1, {1, 20}]

{1.84118,5.33144,8.53632,11.706,14.8636,18.0155,21.1644,24.3113,27.4571,
 
30.6019,33.7462,36.89,40.0334,43.1766,46.3196,49.4624,52.605,55.7476,58.89,
  62.0323}

Alternatively, if your implementation does not work with BesselJZeros:

g[z_] := Evaluate[D[BesselJ[1, z], z]]; z /. Table[FindRoot[g[z] == 0,
{z, n Pi}], {n, 20}]

{1.84118,5.33144,8.53632,11.706,14.8636,18.0155,21.1644,24.3113,27.4571,
 
30.6019,33.7462,36.89,40.0334,43.1766,46.3196,49.4624,52.605,55.7476,58.89,
  62.0323}

Bob Hanlon

In a message dated 9/28/98 11:31:26 PM, meier at tomo.uni-bremen.de wrote:

>I'm trying to find the first 20 roots of the derivation of a
>Besselfunction of the first kind,
>first order.  The BesselJPrimeZeros-function doesn't work while for
>example
>BesselYPrimeZeros does.
>I'm working with mathematica3.0 on a sparc 10 computer.
>
>Example for in- and outputs:
>
>In[31]:=
>BesselYPrimeZeros[1,{1,3}]
>
>Out[31]=
>{3.68302,6.9415,10.1234}
>
>but:
>
>In[32]:=
>BesselJPrimeZeros[1,{1,3}]
>
>Out[32]=
>BesselJPrimeZeros[1,{1,3}]


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