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MathGroup Archive 2007

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Re: Simplifying expressions containing Bessel functions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76892] Re: Simplifying expressions containing Bessel functions?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 29 May 2007 05:05:09 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <f3dpbp$ft0$1@smc.vnet.net>

AES wrote:
> 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] )
> 

FullSimplify or FunctionExpand will do it [1]. For instance,

In[1]:=
D[x BesselJ[1, x], x]
% // FullSimplify
%% // FunctionExpand

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

Out[2]= x BesselJ[0, x]

Out[3]= x BesselJ[0, x]

Regards,
Jean-Marc

[1] "Working with Special Functions",
Documentation Center: tutorial/WorkingWithSpecialFunctions, Web:
http://reference.wolfram.com/mathematica/tutorial/WorkingWithSpecialFunctions.html


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