in reply to http://www.mapleprimes.com/questions/123502-Once-Again-An-Asymptotic-Series-Problem#comment123641
(because comments do not give updates to a thread ...)

Khan,

I guess you mean eq (3) in your attached pdf?

Sorry, my knowledge about DEs is too much limited for a reasonable answer,
may be others can help - but for that it would be better to open a new thread
with a specific question (this one here is becoming quite long now and usually
nobody would step in, as s/he would have to read everything before).

For checking symbolical solutions there commands in Maple like ?odetest

But best would be to start a new thread

I want to bet: it has roots

Here some animated plot, it seems that for increasing lambda (=your lower case L)
there may be no solution for negativ R3 - could that be?

# using the notations in your sheet

Digits:=15;
combine(((subs(S0=S01,parvals,A0))),exp):
v:=convert(%, rational);

eval(v, l=0) indicates there is a division by l

series(v, l=0, 1);

This gives fct(R3)/l + terms of higher orders

But something like R/a does not give a reasonable result
for asympt(%, a)

Guess you need to work with v*l ...

PS: you should avoid variables like l (lower case L)
they are easily mixed up with the constant 1 (=2/2)

restart;
interface(version);
StringTools:-FormatTime("%Y-%b-%d"); # now
Digits:=floor(evalhf(Digits));

  Classic Worksheet Interface, Maple 15.01, Windows, Jun 1 2011, Build ID 635520
                            "2011-Jul-01"
                             Digits := 15

g:=x^3 - 3*2^x + 3;
B:=[RootFinding:-Analytic( g, x, re=-100..100, im=-100..100 )]:
plots:-complexplot(B,  style=point, symbolsize=20);

use the real (usually named "classical") interface and type in
the correct expression, using the multiplication sign

x^2 * sin(x)

Does it work then?

Besides the nice rule shown by Alejandro:

simplify(A,size) usually works quite well.

PS where I never would use a variable L written in lower case, it displays as the number 1

Hi - for me the file does not work, it hangs up

exponential is exp, not and suppressinf multiplication signs is a risk ...

Can you provide in 1D input or as classical sheet

Or the original ...

Otherwise said: the Standard is a trap (I almost never use it)

There is no 2 dim Pade directly in Maple as far as I know

edited: change Q:= ..., not Q(x,t):= ... delete erverything after that
and write lprint(Q) to see, how it is understood.

The output of lprint will be lengthy, but may be I can read that,
if you upload that new file

upload it as file, nobody would type that in ...

collect( - , exp ) etc comes to my mind

what is meant by "approximate"

why shorter - what you are going to do with that 'numerical' expression?

I am oldish. And insist in privacy, if ever possible (having no 'smart' phone, BTW).

Though I would not mind, that Google, Apple and Friends would know my license
key and more. Most important would be, that I have Maple at my fingertips, sure.

Your x-values are equal spaced, so I do not care for them. And if you substract
the mean from your y-values and divide by twice their range maximum - minimum,
naming them Y, then you have

Y:= map( y -> (y-mu)/alpha*2, list2);
plots:-listplot(Y):
plots:-listplot(Y, style=point, color=red, symbolsize=20):
plots:-display(%,%%);

Looking at that graph one sees 'overshootings' and to capture these you either
want to cut them off or need a second sinus (are they really measurement errors).

I guess you will one more, 3rd component as well.

One can use pskill.exe from PsTools, http://technet.microsoft.com/en-us/sysinternals/bb896649

That however does not store the sheet before.

Alec, you can have my commenter badge ...

my interest in contributing here seriously dropped to zero over the last months ..

It is my attitude, that indexing is just a special notation for a function
(here: defined on some Naturals), hence not needed. Anyway:

for j from 1 to 2 do
  x+y^(j);
  f[j]:=unapply(%, x,y);
end do;

f[2](u,v);
                                     2
                                u + v

f[3](a,b);
                              f[3](a, b)

f:= (j,x,y) -> x+y^j;

f(2,x,y);
                                     2
                                x + y