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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