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MathGroup Archive 2007

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Re: Simplify by Recurrence Relations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75794] Re: [mg75753] Simplify by Recurrence Relations
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 10 May 2007 05:26:19 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

expr=D[BesselJ[2,x],x]

(1/2)*(BesselJ[1, x] - 
   BesselJ[3, x])

expr//FullSimplify

BesselJ[1, x] - (2*BesselJ[2, x])/x

expr//.BesselJ[n_/;n>1,z_]:>
      2(n-1)/z BesselJ[n-1,z]-BesselJ[n-2,z]//
  Simplify

(2*x*BesselJ[0, x] + (x^2 - 4)*
    BesselJ[1, x])/x^2


Bob Hanlon

---- Mr Ajit Sen <senra99 at yahoo.co.uk> wrote: 
> Dear Mathgroup,
> 
>   Could someone please show me how to simplify a 
>   function by using its recurrence relations. 
>  
>   As a simple example, let's take the Bessel
> recurrence
>   relation
> 
>      BesselJ[n+1,z]= 2n/z BesselJ[n,z]-BesselJ[n-1,z].
> 
>   How do I get Mathematica (5.2 !) to evaluate
> 
>                D[BesselJ[2,x],x]
> 
>   as   (1-4/x^2)BesselJ[1,x]+ 2/x BesselJ[0,x]
> 
>   instead of (BesselJ[1,x]-BesselJ[3,x])/2 ?
> 
>   [Basically, reduce the order to 0 &/or 1, so that
> all
>   J0 and J1 can be factored out later.]
> 
>   Thanking you in advance.
> 
>   Ajit.
> 
> 
> 
> 		
> ___________________________________________________________ 
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