@Hullzie16 
Thanks, but sorry, you are addressing a totally different problem. I know how to take the limit of f[4], the problem is taking the limit of the boundary value f[4](0) WITHOUT taking the limit of f4 also.
The solution makes no sense w.r.t the problem I posted as you altered my question fundamentally.

@acer 
Thank you for the answer.

That is utterly weird, you dont want to take the limit of the function f[4] itself and just the boundary value f[4](0).

This is akward as I now have to do hand-edits for boundary values which are asymptotic to infinity.

Maple needs to fix this.

Boundary values are staple, and need to be able to be manipulated like any variableby e.g. the limit function.

Apparently not so.

@Carl Love 
Thank you very much, this solves it for me and I awarded you the solution.

No way I could have figured that out from the manual.

How did you find out about the existence of this ?

@Mariusz Iwaniuk 
Agreed it works, but the user should not really have to manipulate the remainder in order to use the expansion. Makes no sense. Maple should do it internally and calculations on remainders should be handled internally.

@nm 
Thank you again for solving my query.
Thank you for clarifying.

This is not a bug, but great oversight from Maple. 
The calculation of the coefficients should be independent of the presence of the remainder.
It is superfluous  to convert to polynomial first, and this should be done by Maple internally.
If coeff is called on an expansion it should ignore the remainder or just state the remainder order if the user wants the coefficient of the remainder or more, or covert to polynomial automatically.
This makes no sense, but this is how it is apparently.

I marked your answer as the solution.

@nm 
Thank you very much for the great help.

Nowhere in the Clunky Maple Help could I find such a clear explanation.

These are super cryptic commands that I will never remember, so I will have to add it to my own help pages.

Thank you very much for taking the time to respond. It is much appreciated, and so much better than the argumentative support from Maple directly.

Your replies solved all my problems, and I marked your answers as solution and gave you all the positive feedback possible.

@nm 
Your solution  works, but in my case, I had to do

evalindets(rhs(sep_theta), 'specfunc'(anything, DESol), F -> op(1, F))

Thanks a lot !!  I will mark your answer as the solution,

Last question, Do you know how to get rid of the superfluos brackets { }  as in one of your solutions ?


This proxy approach by maple creates so much trouble for my workflow, and you always have to peel onions to get your docuemnt fully automated.
 

@nm 
I am using Maple 22, so I dont know if that is very old to your standards.

@nm 
Thank you very much !
The following should solve my problem.

@Scot Gould 
Thanks, you might have just solved my problem.
I'll check

@nm 

@ecterrab 

It baffles me how

" restart;

with(Physics);
 d_[alpha](Christoffel[~alpha, mu, nu]) - d_[nu](Christoffel[~alpha, mu, alpha]) + Christoffel[~beta, mu, nu]*Christoffel[~alpha, beta, alpha] - Christoffel[~beta, mu, alpha]*Christoffel[~alpha, nu, beta]

"

apparently, is soooo difficult for a Maplesoft employee to cut and paste the above into a worksheet.

Anyway, dont bother, I am tired of arguing.

The LaTeX conversion in Maple is basically entirely bunk.

It never worked properly in previous versions and now in Version 2022 it exports only the headers, with no equations or anything resembling the content of my worksheets.

It's really not working for LaTeX export.

@ecterrab 

I's ok, if you dont want to help I am perfectly fine with it.

I am not willing to post worksheets that are pre-publication, and you are intentionally trying to make me do that.

I posted the problem clearly, with an example. Just contract what I gave you.

right here for you.

d_[alpha](Christoffel[~alpha, mu, nu]) - d_[nu](Christoffel[~alpha, mu, alpha]) + Christoffel[~beta, mu, nu]*Christoffel[~alpha, beta, alpha] - Christoffel[~beta, mu, alpha]*Christoffel[~alpha, nu, beta]

It is that easy if you know how to cut and paste. It is easy to learn.

And no, the help pages you listed does not show contraction of my example in my original post in any way. I am familiar with all of them and  read them on and off for three days straight. That is just how it is.

Let someone else try who are willing to solve the problem. I would really appreciate that.

@ecterrab 

As I said, the Maple bug is not part of my question. I will contact Maple directly about that as it is an obvious bug that cannot be fixed here.

Otherwise, I posted a simple definition of the Ricci tensor.

You do not need more.

You paste what I copied above into a new worksheet, and add what you want in the preamble and show me how to contract over the alpha and beta indices. simple as that.

No need for cluttering worksheet.

I went through their Tensor/differential Geometry and Physics help pages, and nowhere could I find to contract tensor expressions.

Easy as that, we dont have to argue.