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Simplify by Recurrence Relations

  • To: mathgroup at
  • Subject: [mg75753] Simplify by Recurrence Relations
  • From: Mr Ajit Sen <senra99 at>
  • 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

     BesselJ[n+1,z]= 2n/z BesselJ[n,z]-BesselJ[n-1,z].

  How do I get Mathematica (5.2 !) to evaluate


  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
  J0 and J1 can be factored out later.]

  Thanking you in advance.


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