Axel Vogt

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20 years, 260 days
Munich, Bavaria, Germany

MaplePrimes Activity


These are replies submitted by Axel Vogt

That may be an undesired sideeffect preventing current spam:

www.mapleprimes.com/blog/bthur/mapleprimestemporarilynotacceptingnewmembers

Thank you, I am in a a bit in an obssesion modus (and find the generic answer quite unsatisfactory here), may be an exorcist might help :-)

PS: happy new year

Thank you, I am in a a bit in an obssesion modus (and find the generic answer quite unsatisfactory here), may be an exorcist might help :-)

PS: happy new year

Thank you, seems have had read your response at that time  with the wrong eyeglasses :-(

Thank you, seems have had read your response at that time  with the wrong eyeglasses :-(

Ok, Thx. I am not that skilled with networking stuff ...

But having an oldish modem there is no traffic if I think I am off, it has a plain old switch :-)

Ok, Thx. I am not that skilled with networking stuff ...

But having an oldish modem there is no traffic if I think I am off, it has a plain old switch :-)

I understand that hesitance. But think "for mantainance ... not possible until 6 Jan" reads better than seeing hundreds of spams

PS: I meant which Trojan and whether poeple here are infected ... but I guess it is a guess

I understand that hesitance. But think "for mantainance ... not possible until 6 Jan" reads better than seeing hundreds of spams

PS: I meant which Trojan and whether poeple here are infected ... but I guess it is a guess

Two possible stupid questions

- If you think that users here have a Trojan would you mind to be somewhat specific?

- Why not shut down automatic registration (but to clean up old or recent regstrations) and allow postings only having already at least n (a bit nasty for new user) until next week ?

 

Two possible stupid questions

- If you think that users here have a Trojan would you mind to be somewhat specific?

- Why not shut down automatic registration (but to clean up old or recent regstrations) and allow postings only having already at least n (a bit nasty for new user) until next week ?

 

... but cleaning up is not the only thing to do ... any plans for the current future?

... but cleaning up is not the only thing to do ... any plans for the current future?

I stumbled into that thread for other reasons, _EnvFormal) and will ignore the
possible bug, as it seems to be not ubiquitous.


Start with the series in 1 (the difference is clear) and change to summing in 0:

  Sum((1+exp(n))/(exp(n)-1),n = 1 .. infinity);
  changevar(n=k+1,%,k); value(%); # with(student)
  b:=unapply(op(1,%),k);
 

                                 1 + exp(k + 1)
                       b := k -> --------------
                                 exp(k + 1) - 1

Define

  a := n -> 1/(exp(n+1)-1);

Then 

  'b(n) = 1 + 2*a(n)';
  is(%);
                          b(n) = 1 + 2 a(n)
                                 true

Since a(n) is positive the sum over b(n) can not converge (and my gut feeling
says: there is not interpretation as a finite value through divergent series
in such a case, but my feeling is quite wrong far too often).

And it should follow, that any acceleration method should respect that (no,
not my feeling, but b(n) = 1 + positive can not be summed numerically in the
usual sense).

 
However Maple finds the sum over a(n) and using 14 Digits one gets:

  Sum(a(n)*1^n, n=0..infinity);  evalf(%);

                           0.82025951154242

Since a(n) quickly approaches 0 there should be no doubt about that.

But here is a cross check, by the so-called Abel-Plana formula (that is why I
switched to start summing in 0), Sum(a(n), n=0..infinity) equals the following:

  'int(a(x),x=0 .. infinity) + a(0)/2 + 
     I*Int((a(I*x)-a(-I*x))/(exp(2*Pi*x)-1), x=0..infinity)';

  %; evalf(%);

                               1
  1 - ln(exp(1) - 1) + 1/2 ----------  + Int(...)
                           exp(1) - 1


                           0.82025951154245


Only the last part needs numerical evaluation and using 'evalc' on its integrand
shows it is actually a real integrand (take evalc(Im(...))). It is oscillating,
but approaches 0 very quickly (take x = 6 to get -.20329770683779e-16).

Which is not a prove, but I was not able to figure out the exact, symbolic value.
May be that follows using Fourier/Laplace methods.

sound cyncial, but a good timing for an attack

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