 |
|
List Archives >
Maple User Group List Archive >
Archive by date >
This Month By Date >
This Month By Topic
[MUG] Bug in sum ?
| [MUG] Bug in sum ? |
|
Author: Jean Brillet
Posted: 28/11/2000 18:19:07 GMT
|
>> From: Jean Brillet
Hi,
Is there a bug in sum() ? (MAPLE 5 and MAPLE 6.01)
> restart:
> Sum(exp(-k)/k,k=1..infinity):%=value(%);
infinity
-----
\ exp(-k)
) ------- = -ln(1 - exp(-1))
/ k
-----
k = 1
This result seems correct but what does the following meens ?
> Sum(exp(k)/k,k=1..infinity):%=value(%);
infinity
-----
\ exp(k)
) ------ = -ln(1 - exp(1))
/ k
-----
k = 1
> evalc(rhs(%));
-ln(exp(1) - 1) - I Pi
>
I expect infinity.
Jean Brillet
http://www.observ.u-bordeaux.fr
Tel : 05 57 77 61 57
Observatoire de Bordeaux
B.P. 89
33270 Floirac (France)
|
| [MUG] Re: Bug in sum ? |
|
Author: Maple Group
Posted: 01/12/2000 20:13:46 GMT
|
Subject: Bug in sum ?
On Tue, 28 Nov 2000, Jean Brillet wrote:
| Is there a bug in sum() ? (MAPLE 5 and MAPLE 6.01)
| > Sum(exp(-k)/k,k=1..infinity):%=value(%);
| infinity
| -----
| \ exp(-k)
| ) ------- = -ln(1 - exp(-1))
| / k
| -----
| k = 1
Totally correct.
| This result seems correct but what does the following meens ?
|
| > Sum(exp(k)/k,k=1..infinity):%=value(%);
| infinity
| -----
| \ exp(k)
| ) ------ = -ln(1 - exp(1))
| / k
| -----
| k = 1
| > evalc(rhs(%));
| -ln(exp(1) - 1) - I Pi
| >
|
| I expect infinity.
The help page for "sum" says:
------------------------------
Note that sum knows about various resummation methods and will thus be
able to give the 'correct' value for various classes of divergent sums. If
one wants to restrict summation to convergent sums, then explicit
convergence checks must be done.
------------------------------
Actually I think this is a bit misleading: Maple is not really using fancy
summability methods, it is just not checking for convergence and thus
uses formulas such as (in this case) sum(r^k/k, k=1..infinity) = -ln(1-r)
outside the region where the sum converges.
I have a procedure "csum" in my Maple Advisor Database that attempts to
check whether a sum converges. For example:
> csum(exp(-k)/k, k);
true
> csum(exp(k)/k, k);
false
See http://www.math.ubc.ca/~israel/advisor
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
Date: Thu, 30 Nov 2000 11:12:16 +0900
To:
From: tanaka
Subject: Fwd: Bug in sum ?
When we evaluate
Sum[Exp[k]/k, {k, 1, Infinity}]
by using Mathematica ver.4, we have a messege
"Sum ::div: sum does not converge";
this must be the one that Monsieur Brillet expects.
Therefore, I think there must be a bug in Sum in Maple.
- - - - - - - - - - - - - - - - - - - - - - - - - - -
ps. If we evaluate
Sum[Exp[-k]/k, {k, 1, Infinity}]
by employing Mathematica ver4, it yields
-Log[1 - 1/e],
which is identical with the result by Maple.
|
Previous by date: [MUG] Re: printing plots with G-4, Roberto A Sussman
Next by date: [MUG] Re: NEWBY with problems with Maple 6.01 and Linux, Desmond Johnston
Previous thread: [MUG] Simplification problem, Carl Eberhart
Next thread: [MUG] NEWBY with problems with Maple 6.01 and Linux, Andre Estel
|
|
|
Datasheet