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