Change variables and expand around new variable (Mathematica)

[ramparts]

I have a differential expression that I want to expand to some order around infinity (it's for calculating weak-field limits in GR). I have two functions, B(r) and n(r), and some expression involving them along the lines of

n[r] (3 r B'[r]^2 - 4 B[r] (2 B'[r] + r B''[r]))

Basically I want to change variables to x=1/r and expand this expression around x=0 to, say, 5th order. This seems like it would be fairly simple, but I must be doing something wrong because Mathematica keeps giving me errors like

General::ivar: "1/r is not a valid variable."

I've tried several ways of doing this, but I'm still learning Mathematica so I'd appreciate having the right way pointed out! Thanks.

(I've also tried expanding around {r,Infinity,5} and just gotten a symbolic result which wasn't useful.)

 

[Stephen Tashi]

I don't have Mathematica, but I suggest that you create a simplified example of this situation and see if error happens. If it does, you can post the example. If it doesn't, it might lead to some other aspect of the problem that you failed to capture in the example.

 

[ramparts]

I think the problem boils down to this: given a differential expression (like the one I posted) I don't know how, in Mathematica, to change variables and have Mathematica do all the chain rule through. I've since learned that Maple can do this (and indeed I've been using Maple for what I need to do) with its dchange function in the PDETools. I wonder how one can get the same functionality within Mathematica.

 

[Stephen Tashi]

I can't help with that. I suggest you ask in the forum section Physics Forums > Other Sciences > Computing & Technology. > Math & Science Software

 

[CellCoree]

Thank you for your question. In order to expand your expression to a certain order around infinity using Mathematica, you can use the following steps:

1. Define your functions B[r] and n[r] using the "Set" command, for example:

B[r_]:= 1/r

n[r_]:= r^2

2. Use the "Series" command to expand your expression to the desired order, using the variable x=1/r and specifying the order as 5:

Series[n[r] (3 r B'[r]^2 - 4 B[r] (2 B'[r] + r B''[r])), {x, 0, 5}]

This will give you the expanded expression in terms of the variable x.

3. You can then substitute back in the original variable r by using the "ReplaceAll" command, for example:

%/.x->1/r

This will give you the expanded expression in terms of the original variable r.

Hope this helps! If you have any further questions, please feel free to ask.