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)

```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]
>
>
>   [Basically, reduce the order to 0 &/or 1, so that
> all
>   J0 and J1 can be factored out later.]
>
>
>   Ajit.
>
>
>
>
> ___________________________________________________________
> To help you stay safe and secure online, we've developed the all new Yahoo! Security Centre. http://uk.security.yahoo.com
>

```

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