Re: Simplify by Recurrence Relations 2

*To*: mathgroup at smc.vnet.net*Subject*: [mg75757] Re: Simplify by Recurrence Relations 2*From*: dimitris <dimmechan at yahoo.com>*Date*: Thu, 10 May 2007 05:06:37 -0400 (EDT)*References*: <f1s3n1$h2g$1@smc.vnet.net>

I forgot to add that now (after addintg the rule!) you have In[40]:= Information["BesselJ", LongForm -> True] "BesselJ[n, z] gives the Bessel function of the first kind J(n, z)."*Button[More..., ButtonData :> "BesselJ", Active -> True, ButtonStyle -> "RefGuideLink"] Attributes[BesselJ] = {Listable, NumericFunction} BesselJ[n_, z_] := 2*(n/z)*BesselJ[n - 1, z] - BesselJ[n - 2, z] /; n >= 2 When you finish with your work don't forget to clear the rule by In[41]:= Clear[BesselJ] Also protect again BesselJ In[46]:= Protect[BesselJ]; In this way you restore the "default" BesselJ In[47]:= Information["BesselJ", LongForm -> True] "BesselJ[n, z] gives the Bessel function of the first kind J(n, z)."*Button[More..., ButtonData :> "BesselJ", Active -> True, ButtonStyle -> "RefGuideLink"] Attributes[BesselJ] = {Listable, NumericFunction, Protected} Cheers Dimitris =CF/=C7 Mr Ajit Sen =DD=E3=F1=E1=F8=E5: > 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 Yaho= o! Security Centre. http://uk.security.yahoo.com