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]

>

>

>   [Basically, reduce the order to 0 &/or 1, so that

> all

>   J0 and J1 can be factored out later.]

>

>

>   Ajit.

>

>

>

>

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