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