Re: I have an operator, How do I DSolve it?

*To*: mathgroup at smc.vnet.net*Subject*: [mg96202] Re: I have an operator, How do I DSolve it?*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Mon, 9 Feb 2009 05:34:34 -0500 (EST)*References*: <gmndhs$s04$1@smc.vnet.net>

Hi, I'm not sure to understand your question, because B[m_, f_] := (D[f[#], {#, 2}] + 1/# D[f[#], {#, 1}] + (1 - m^2/#^2) f[#]) & does already what you want. If you don't like to have the Function[{r},__] and prefer a Slot[] argument G[m_, f_] := Block[{r}, DSolve[B[m, f][r] == 0, f, r][[1]] /. Function[{r}, expr_] :> Function @@ {expr /. r -> Slot[1]}] Regards Jens Aaron Fude wrote: > Hi, > > I have defined a differential operator, but what's the syntax for > using it in DSolve? > > I have the Bessel operator > > B[m_, f_] := (D[f[#], {#, 2}] + > 1/# D[f[#], {#, 1}] + (1 - m^2/#^2) f[#]) & > > It's the Bessel operator for now, but I will soon replace it with a > different one. This is for testing puposes only. > > Now, how do I use it in DSolve? > > So far I use > > DSolve[S''[r] + 1/r S'[r] + (1 - m^2/r^2) S[r] == 0, S[r], r] > > but that's not a good solution because I have to different expressions > for the same thing. I want to used B only. > > Many thanks in advance, > > Aaron >