Re: Simplify by Recurrence Relations
- To: mathgroup at smc.vnet.net
- Subject: [mg75788] Re: Simplify by Recurrence Relations
- From: Norbert Marxer <marxer at mec.li>
- Date: Thu, 10 May 2007 05:23:08 -0400 (EDT)
- References: <f1s3n1$h2g$1@smc.vnet.net>
On 9 Mai, 11:19, Mr Ajit Sen <senr... 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 Hello You could apply repeatedly (i.e. //.) the substitution for n>1 BesselJ[n_, z_] :> (2(n - 1)/z BesselJ[n - 1, z] - BesselJ[n - 2, z]) /; n > 1 The following D[BesselJ[2, x], x] //. BesselJ[n_, z_] :> (2( n - 1)/z BesselJ[n - 1, z] - BesselJ[n - 2, z]) /; n > 1 // Expand will give (except factoring out) what you want, i.e. (2*BesselJ[0, x])/x + BesselJ[1, x] - (4*BesselJ[1, x])/x^2 Best Regards Norbert Marxer