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MathGroup Archive 2007

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Re: Simplify by Recurrence Relations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75797] Re: Simplify by Recurrence Relations
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 10 May 2007 05:27:57 -0400 (EDT)
  • References: <f1s3n1$h2g$1@smc.vnet.net>


Hi Ajit,

you could e.g. define a rule for BesselJ that reduces the order. E.g:

Unprotect[BesselJ];

BesselJ[n_/;n>1,z_]=2n/z BesselJ[n-1,z]-BesselJ[n-2,z];

now try:

D[BesselJ[2, x], x] // Simplify

hope this helps, Daniel



Mr Ajit Sen 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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