csgn

[boi]

X(z) is a function defined (properly, somewhere in the beginning of my Maple
sheet) as

X(z);
160801 1
---------- ---------------------
1600000000 / 201\2 / 201\2
|z - ---| |z + ---|
\ 200/ \ 200/

> residue(X(z)*z^(-k),z=-201/200);

160801
- --------------------
41785364505600000000

-6432000000 %1 k - 6432000000 %1
------------------------------------------------------
/ 201 \
exp(k |ln(---) - I csgn(1/200 I (200 z - 201)) Pi|) %1
\ 200 /

/ 201 / 201\ \
%1 := exp(k |ln(---) - I csgn(I |z - ---|) Pi|)
\ 200 \ 200/ /

How can the residue depend on z? Maybe I have to take into account the fact
that k is a positive integer. How do I do that? Do I get a normal result
then?

Thanks

Boi

[C W]

The value You are looking for is :
R := 160801/6496480800*200^k*(1+k)/(201^k)/exp(I*k*Pi);

Chris

[Carl Devore]

C W <sylve...@ns.sympatico.ca> wrote:

> boi wrote:
> > X(z);
> > 160801 1
> > ---------- ---------------------
> > 1600000000 / 201\2 / 201\2
> > |z - ---| |z + ---|
> > \ 200/ \ 200/
> >
> > > residue(X(z)*z^(-k),z=-201/200);
> >

> > How can the residue depend on z? Maybe I have to take into account the fact
> > that k is a positive integer. How do I do that? Do I get a normal result
> > then?
>

> The value You are looking for is :
> R := 160801/6496480800*200^k*(1+k)/(201^k)/exp(I*k*Pi);

How about just 16081/6496480800*(-200/201)^k*(1+k).
It is strange that the commands `residue` and `series` do not realize
that regardless of whether the csgn is 0 or 1, the answer is the same.
These commands do not seem to be able to make use of an integer
assumption on k.

[Alec Mihailovs]

"Carl Devore" <dev...@math.udel.edu> wrote in message
news:3a64b911.03092...@posting.google.com...

I got the answer using following series of commands,

residue(X/z^k,z=-201/200) assuming z>201/200;
simplify(%);
combine(%);
expand(%) assuming integer;
factor(%);

k k
160801 200 (-1) (k + 1)
-------------------------
k
6496480800 201

Alec Mihailovs
http://webpages.shepherd.edu/amihailo/