A simple - but handwaving - 'explanation' is to refer to integral ~ sum.

Is it the bug?

Your problem is over the Reals, your input is over the Complex and from what you
say I would start from 

 f(x): 
 subs(Dif=1e-9 * d, %): # scaling, now estimate for d
 evalc(Re(%)):          # assumes x, d are Reals
 simplify(%, zero):     # kick off stuff not needed here
 simplify(%, size):     # house keeping 
 g:=unapply(%,x);

Note however, that you only have 3 points, in which you have 'reasonable data':
if I see it correctly, then y=0 can not be possible, thus do not feed them.

May be you need to fit against abs( g(x) ) or similar.

One improvement might be, to fit for ln(y) = ln(x)

Your problem is over the Reals, your input is over the Complex and from what you
say I would start from 

 f(x): 
 subs(Dif=1e-9 * d, %): # scaling, now estimate for d
 evalc(Re(%)):          # assumes x, d are Reals
 simplify(%, zero):     # kick off stuff not needed here
 simplify(%, size):     # house keeping 
 g:=unapply(%,x);

Note however, that you only have 3 points, in which you have 'reasonable data':
if I see it correctly, then y=0 can not be possible, thus do not feed them.

May be you need to fit against abs( g(x) ) or similar.

One improvement might be, to fit for ln(y) = ln(x)

The following works (for the uploaded example and the shorter one given by Preben Alsholm):

radnormal(numer(Z))/radnormal(denom(Z)): 
radnormal(%):
ZZ:=simplify(%, size):
'Z=ZZ'; is(%);
                                Z = ZZ
                                 true

length(Z), length(ZZ);
                             151121, 2442

radnormal(ZZ): length(%);
                                18985

I guess it is meant: answer by 'k' for the following

(n+k) mod n; 
simplify(%) assuming n::posint,k::posint;

I guess it is meant: answer by 'k' for the following

(n+k) mod n; 
simplify(%) assuming n::posint,k::posint;

If however it is your task to write a program, then you may
wish to have a look at http://en.wikipedia.org/wiki/Legendre_polynomials

If however it is your task to write a program, then you may
wish to have a look at http://en.wikipedia.org/wiki/Legendre_polynomials

mutmurat, it is on you ... But nobody would not do it by evalf.

For large n your expression is ~ n * (-1)* (n^3)*4 / n^4 ... and so on.
But nobody would that type in.

And if you have hundreds of expressions the game is the same.

The command you are probably looking for is limit( f(n)/n, n=infinity ).

mutmurat, it is on you ... But nobody would not do it by evalf.

For large n your expression is ~ n * (-1)* (n^3)*4 / n^4 ... and so on.
But nobody would that type in.

And if you have hundreds of expressions the game is the same.

The command you are probably looking for is limit( f(n)/n, n=infinity ).

As pagan says ... I never understand, why that's not clearly stated
at the registration pages (or is it?)

Was puzzling a bit more, the following is my current favourite

LerchPhi(a,b,z) = 
  z^(-b) + 1/GAMMA(b)*'laplace'( s^(b-1)*(1/(1-a*exp(-s))-1),s, z), 

  laplace(fct(s),s, z) = Int(fct(s) * exp(-s*z), s = 0 .. infinity)

where for |a| < 1 and double precision one can cut off the Laplace integral at
s ~ 37. That works for complex situation as well, it covers a=9/10, b=11, z=2001
(where Maple seriously fails) or a=0.99, b=0.1, z=2.1 (where the trigonometric
formulation gives up [since b < 1 as I would guess]).

For b = integer it seems that the linked solution by Jentschura et al is really
fine (but got lost in the non-cited theory, why acceleration here works, the
magic word may be 'complete monoton' [I am not used to that]).

And since I do not know how to enforce Maple's compiler to 'include' stuff
I do not provide a DLL solution to be produced by Maple only

@icegood 

I still do not get it ... but is your idea something like
having a 'convex hull', some 'tube' around the function ?

May be not for (small) integer powers, but rationals, if one
wants to generate code to be compiled.

However it is possible by using "evalindets"

May be not for (small) integer powers, but rationals, if one
wants to generate code to be compiled.

However it is possible by using "evalindets"