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.
>
>
>
>
> ___________________________________________________________
> To help you stay safe and secure online, we've developed the all new Yahoo! Security Centre. http://uk.security.yahoo.com
>