@Rouben Rostamian  

After posting the solution I have also found Kurtz' article.
Note that "=" also can be used to find a simple sequence (with smaller 1/a[n]) namely:
a[n] = 2^( - n*(n - 1) ), n>0,  a[0]=1/2.

subsop(2=s,J)

replaces the second operand of J (which is  s = xi1 .. L1)  with   s.

See in the help file:
?subsop

@digerdiga

@mimi990 

fun11 is actually a vector (of dimension 1) containing the integral. So, fun11[1]  is the integral itself.
The subsop converts the definite integral into an indefinite one.

@9009134 

This function is also non-periodic. 

In general, if two continuous nonconstant periodic functions f, g : R --> R have incommensurable periods (i.e. their ratio is irrational) then f + g is non-periodic.

I don't know what you mean by minimal period in this case; d is not periodic. The periods of the two terms are incommensurable, there is no common period.

@Kitonum 

It's impossible to get uniform approximations this way. E.g. for t=40800*Pi..40800*Pi+3  the difference is very large.

@mmcdara 

This is another function. OP says f(t)=t^2 for t in [0,2*Pi]. It has discontinuous periodic extension.
Yours is continuous.

@mmcdara 

Sorry, but you are confusing "Fourier series" with "Fourier transform".

@mmcdara 

But sum(1/u, u in L) is nonsense in Maple (just try it for L:=[1,2]). Any such nonsense will produce infinity due to the empty catch clause. I think that you meant add instead.

@mmcdara 

The standard periodic extension of a function f defined in [0,T) is simply x |--> f(x - floor(x/T)*T).
It's not about distributions here. In the theory of Fourier series, the integrability is in [0,T). I think that you have in mind the Fourier transform.

@Zeineb 

Have you checked for all b?

@tomleslie 

Nice, vote-up!
I'd suggest to insert in your code

nE,nV := NumberOfEdges(T), NumberOfVertices(T);
# Produce all subgraphs of G which have the same number of edges and vertices as the "test" sub-graph T
U:=choose(Edges(G),nE): nops(%);
U1:=select(t -> (nops(`union`(t[]))=nV), U): nops(%);
gL:= Graph~(U1): nops(%);

in order to reduce the number of candidates.
 

@Carl Love 

The Squeezing Theorem cannot be used here.
If   limit(liminf(f(x,y), y=0), x=0)  and  limit(limsup(f(x,y), y=0), x=0)  exist and are equal,
it does not imply the existence of limit( limit(f(x,y), y=0), x=0); and actually it does not exist.

BTW, it would be nice to have liminf and limsup in Maple.

@acer 

A very nice and professional patch (a single line of code added). I hope to be included in the next Maple update.

@9009134 

Maple cannot help much here because the only transforms are integrations by parts for generic functions, and  some other functions (e.g. I_0, I_2)  just appear from nowhere. These are easier to do by hand, but as I said above, some integrals are missing from some terms. [The final result could be correct though, if the δu etc are chosen to be 0 on the boundary (so, these terms become 0), but these aspects must be examined carefully].

In conclusion, what is needed here is (proper) maths, not Maple.