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 >