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