Peter_Parker, Thx for your email - but please use that board for ongoing discussions ... Best, Axel

Asymptotics for what?

assume(0 <= v);

HankelH1(v,x);
MultiSeries:-asympt(%,x, 2); 
eval(%, O=0);
convert(%, exp);

Does it give what you are looking for?

LambertW(x);
convert(%, Wrightomega);
subs(ln(x) = t, %);
asympt(%, t,2);
subs(t=ln(x), %);

                                  ln(ln(x))       1
              ln(x) - ln(ln(x)) + --------- + O(------)
                                    ln(x)            2
                                                ln(x)

find a classical sheet attached

Problem-With-Math-Mo.mws

It works for me, both with Maple 12 and Maple 15 (classical and standard interface):

restart; interface(version);

  Classic Worksheet Interface, Maple 15.00, Windows, Mar 20 2011, Build ID 582305

with(DifferentialGeometry):
DGsetup([x],M):
ExteriorDerivative(x^2);

                                2 x dx
lprint(%);

 _DG([["form", M, 1], [[[1], 2*x]]])

difference quotients ... or a (polynomial?) fit ... or (locally) approximating by splines and differentiating

may be you want to 'filter' outliers first

1. Set it to 1 ... :-) Or end with a double point + use the print command.
Otherwise said: do you really need such?

2. Providing such would probably result in endless support requests.
And without deep experience there is a good chance, that one is not
even aware of side effect and impacts.

For any 2 <= j <= 2011 take the largest of such a factor of j and take the product,
which is to add the exponents.

That way I get k = 2002 by brute counting, using 'ifactors', resulting in a 603 digit
integer for 2^k.

arctanh(x); A:=evalc(%); # decompose in real + imaginary, assuming x is Real

simplify(A, size) assuming 1 <= x;
                                   2
                            (x + 1)
                     1/4 ln(--------) - 1/2 I Pi
                                   2
                            (x - 1)

simplify(A, size) assuming x <= -1;
                                   2
                            (x + 1)
                     1/4 ln(--------) + 1/2 I Pi
                                   2
                            (x - 1)

try to avoid indexed variables (and be aware, that array (lOWER cASE) is outdated)

and use multiplication signs

Perhaps the following does what you want

  phi:= (q,x) -> p*q*x;

  phi(1,2);
                                 2 p
  phi(2,2);
                                 4 p

Do You need something like this, ?IntegrationTools[Change],
http://www.maplesoft.com/support/help/Maple/view.aspx?path=IntegrationTools%2fChange

Change(Int(...), x = a + xi, xi)

Numerical I get it as Pi/2 for f(x) = x^2  with 14 places.

Will say more after cleaning up my sheet ... though not analytical.

Edited: err ... typo .. 2/Pi ... see below

Unfortunately you can not write or get -1 < x < 1 (except, that it may look as if it would be so).

However something similar (but not that nice) using ranges, like:

  assume(y=0, x>-1, x<1); getassumptions(x);

                  {x::RealRange(Open(-1), Open(1))}

I guess that leading coefficient = 1 is meant, otherwise assume it

If a is the only zeros of a polynomial in: how can you write it down?
If a,b,c are the only zeros of a polynomial in: how can you write it down?

Recall how the number of zeros of a polynomial and degree are related,
if one works over the complex numbers and then write down the 1st answer

Recall how the complex zeros of a parabola are related - can you express
that by complex conjugation?

Recall how complex zeros of a polynomial are related or formulate a guess
and look it up in your lectures.

For the rest you may remember school and try to use Maple.

In any case: show up what have achieved and done so far before asking.

I have not checked the concurrent status, but Maple provides manuals as pdf,
http://www.maplesoft.com/documentation_center/