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Simplifying expressions containing Bessel functions?

• To: mathgroup at smc.vnet.net
• Subject: [mg76845] Simplifying expressions containing Bessel functions?
• From: AES <siegman at stanford.edu>
• Date: Mon, 28 May 2007 01:08:36 -0400 (EDT)
• Organization: Stanford University

Is there any kind of Simplification procedure in Mathematica that will 
somehow apply the recursion relations between Bessel functions of orders 
n-1, n and n+1 to eliminate the highest orders in an expression?

I realize this is not a simple topic -- but it would be nice if

   D[x BesselJ[1, x], x]

would yield

   x BesselJ[0, x]

rather than

   BesselJ[1, x]  +  (x/2) ( BesselJ[0, x] - BesselJ[2, x] )

• Follow-Ups:
  • Re: Simplifying expressions containing Bessel functions?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>