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