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[MUG] problems with series()
| [MUG] problems with series() |
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Author: Raya Khanin
Posted: 28/02/2000 12:53:07 GMT
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>> From: Raya Khanin
I have a lot of problems with series() command in Maple release 4.
For example consider function
y := t->-t+sqrt(t^2-1/p);
and expand it in series near point t=-1/sqrt(p), where expression t^2-1/p
changes its sign.
Commands
series(y(t), t=-1/sqrt(p), 1); series(y(t), t=-1/sqrt(p), 2);
produce different results:
>series(y(t), t=-1/sqrt(p), 1);
1 / 2 \1/2 / 1 \1/2 1
---- + |- ----| |t + ----| + O(t + ----)
1/2 | 1/2| | 1/2| 1/2
p \ p / \ p / p
> series(y(t), t=-1/sqrt(p), 2);
/ 2 \1/2 / 1 \1/2 / 2 \1/2 1/2 / 1 \3/2
|- ----| |t + ----| - t - 1/4 |- ----| p |t + ----|
| 1/2| | 1/2| | 1/2| | 1/2|
\ p / \ p / \ p / \ p /
/ 1 \5/2
+ O(|t + ----| )
| 1/2|
\ p /
with the main term equal 1/sqrt(p) for the first case, and 0 for
the second case. Obviously, the first result is correct:
> subs(t=-1/sqrt(p), y(t)); 1/sqrt(p);
Is it because series() command does not work very well? Or am I doing
something
wrong? Does series() command in release 5 work better? Thanks very much
Raya Khanin
DAMTP
University of Cambridge
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| [MUG] Re: problems with series() |
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Author: Robert Israel
Posted: 02/03/2000 22:27:58 GMT
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>> From: Robert Israel
Actually, both results are correct. Note that the difference
between them is
1 1 / 2 \1/2 1/2 / 1 \3/2
---- + O(t + ----) + t + 1/4 |- ----| p |t + ----|
1/2 1/2 | 1/2| | 1/2|
p p \ p / \ p /
/ 1 \5/2
- O(|t + ----| )
| 1/2|
\ p /
which is O((t+1/sqrt(p)). I think what's misleading you is that
the order-2 result simplifies 1/sqrt(p) -(t+1/sqrt(p)) to -t.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
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