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MathGroup Archive 1999

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Re: DSolve Bessels

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19145] Re: DSolve Bessels
  • From: Hendrik van Hees <h.vanhees at gsi.de>
  • Date: Thu, 5 Aug 1999 23:58:47 -0400
  • Organization: GSI Darmstadt
  • References: <7ob7ld$348@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Alberto Verga wrote:
> 
> Mathematica 3 seems to be not able to show that J_1(x) is solution of
> the Bessel equation:
> 
> in: yy=BesselJ[1,x]
> 
> in: Simplify[D[yy,{x,2}]+D[yy,x]/x+(1-1/x^2)yy]
> 
> out: 1/(4x^2) (x^2 BesselJ[-1, x] + 2 x BesselJ[0, x] - 4 BesselJ[1, x]
> +
>       2 x^2 BesselJ[1, x] - 2 x BesselJ[2, x] + x^2 BesselJ[3, x])
> 
> Using trivial transformations one gets 0, Mathematica does it not.
> One obtains the correct answer (out: 0) in other systems.

Sure, this is one of the definitions of the Bessel function. Use
FullSimplify instead of Simplify and Mathematica 3.0 immediately answers
0 as expected (I'm using Mathematica 3.0 for Students under Linux).


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