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.
>
>
>
>
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