Re: DSolve Bessels

*To*: mathgroup at smc.vnet.net*Subject*: [mg19143] Re: DSolve Bessels*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Thu, 5 Aug 1999 23:58:46 -0400*Organization*: University of Western Australia*References*: <7ob7ld$348@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Alberto Verga wrote: > Mathematica 3 seems to be not able to show that J_1(x) is solution of > the Bessel equation: > > in: yy=BesselJ[1,x] > > in: Simplify[D[yy,{x,2}]+D[yy,x]/x+(1-1/x^2)yy] > > out: 1/(4x^2) (x^2 BesselJ[-1, x] + 2 x BesselJ[0, x] - 4 BesselJ[1, x] > + > 2 x^2 BesselJ[1, x] - 2 x BesselJ[2, x] + x^2 BesselJ[3, x]) > > Using trivial transformations one gets 0, Mathematica does it not. > One obtains the correct answer (out: 0) in other systems. You need to use FullSimplify (or Simplify and FunctionExpand) in 3.0 or 4: Mathematica 3.0 for Digital Unix In[1]:= FullSimplify[(1 - 1/x^2)*BesselJ[1, x] + D[BesselJ[1, x], x]/x + D[BesselJ[1, x], {x, 2}]] Out[1]= 0 ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________