Help with project needed

*To*: mathgroup at smc.vnet.net*Subject*: [mg96619] Help with project needed*From*: Aaron Fude <aaronfude at gmail.com>*Date*: Tue, 17 Feb 2009 06:27:26 -0500 (EST)

Hi, I'm about to attempt a project in which so many Mathematica related things are unclear to me that I will describe the project, rather than try to ask individual questions. Suppose that C is a function of alpha, but it also depends on a parameter epsilon, so I think of it as C[epsilon][alpha] -- but I'm OK with it if the implementation treats C as a function of two variables. This C is given. It's complicated, but one could easily obtain a series for it in epsilon. Now, I have the following operator that acts on functions of "r", and "alpha" (d is partial): L = C''(1-C')/(1+C^2) * d/dr + C'(1-C'') /(1-C')* d/dalpha For a given function f[r, alpha], I need to take successive orders in epsilon of the operator and apply it to f. I realize that for a given function f, I can form L[f] and the do Series[L[f], {epsilon, 0, 5}]. However, I'm very interested in seeing the operator decomposed into a series. I want to be able to say, here's the epsilon term of the operator, here's the epsilon squared term, and so forth. Can this be done. Can I decompose L into a series: L = L0 + L1 + L2 + .... and then be able to apply Ln to f? Many thanks in advance, Aaron