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Simplify by Recurrence Relations

• To: mathgroup at smc.vnet.net
• Subject: [mg75753] Simplify by Recurrence Relations
• From: Mr Ajit Sen <senra99 at yahoo.co.uk>
• Date: Wed, 9 May 2007 04:49:00 -0400 (EDT)

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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