RE: Differential operators, Help

*To*: mathgroup at smc.vnet.net*Subject*: [mg25366] RE: [mg25332] Differential operators, Help*From*: "David Park" <djmp at earthlink.net>*Date*: Sun, 24 Sep 2000 03:01:33 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Bill, What about this: op = (D[#1, {#2, 2}] + #2 D[#1, #2]) &; op[f[z], z] op[%, z] z*Derivative[1][f][z] + Derivative[2][f][z] 2*Derivative[2][f][z] + z*Derivative[3][f][z] + z*(Derivative[1][f][z] + z*Derivative[2][f][z] + Derivative[3][f][z]) + Derivative[4][f][z] Which is the same as D[Derivative[2][f][z] + z*Derivative[1][f][z], {z, 2}] + z*D[Derivative[2][f][z] + z*Derivative[1][f][z], {z, 1}] David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > -----Original Message----- > From: Bill Bertram [mailto:wkb at ansto.gov.au] To: mathgroup at smc.vnet.net > 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 > > > > > >