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MathGroup Archive 2000

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Re: Differential operators, Help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25392] Re: Differential operators, Help
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 29 Sep 2000 01:06:24 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <8qhnai$j12@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

if you don't like

In[]:=P = D[#1, {#2, 2}] + #2*D[#1, #2] &
In[]:=P[f[z], z] 
z*Derivative[1][f][z] + Derivative[2][f][z]


can you explain what you want ? You can't stop the evaluation so that
P[f,z] evaluates but   P[P[f,z],z] not and so it is impossible to get

> P[ P[f[z],z], z]  -> (f''[z] + z f'[z])''+ z (f''[z] + z f'[z])'

The best you can get is
Out[6]//OutputForm=
              (3)                             (3)
2 f''[z] + z f   [z] + z (f'[z] + z f''[z] + f   [z]) + 
 
   (4)
  f   [z]

Regards
  Jens

Bill Bertram wrote:
> 
> Hi group,
> 
> This should be relatively easy, but after several tries I have not been able
> to do it.
> 
> I want define a differential operator in the following way. Let Dx and Dx2
> denote the operators for first and second order differentiation with respect
> to x. I want P to be an operator which depends on x,  Dx and Dx2.
> 
> For example, with
> 
>                   P = Dx2 + x Dx
> 
> I want P[f[z],z] = f''[z] + z f'[z].
> 
> This much I can do, but I cannot find a method which also gives the
> following result,
> 
> P[ P[f[z],z], z]  -> (f''[z] + z f'[z])''+ z (f''[z] + z f'[z])'
> 
> Or more generally, if I have two such operators P and Q I want the correct
> result from expressions such as
> 
>       P[ Q[f[x],x], x]
> 
> Any suggestion will be greatly appreciated.
> 
> Bill


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