       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[f][z] + Derivative[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//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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