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