Directly at the end of the initial post you can click the link 'subscribe post', which should do that.

Ok.

Trying again that weekend the URL did not load at all (migration? testing?) before any login and if I 'ping' it, then it is present - response at ~ 100 - 200 msec, but almost every second ping is lost and timed out.

So I did not continue to test (besides the false login)

What comes to my mind (though I do not have a solution):

1) In the integral form the problem is something like a Laplace integral (it does not matter much, where you start) or oscillating with slowly decaying amplitude (may be substract 1 from exp( ln(x)/x) ). Even if I generally like Mathar's contributions at the usenet: I think the way is not to slice into intervals and accelerate, but to deform the integration path to reduce oscillation and use contour integration (+ estimate to infinity).

2) For the relation between integral and sum form I would look for 'Abel-Plana formula' and related stuff.

But I do not have a solution for your favourite theme.

Is it to (numercial) compute 

  Lim( Int( exp( I*Pi*x + ln(x)/x ), x= 1 .. 2*n ), n = infinity ) 

according to Robert Israel's comment or what?

in the beginning there is some traffic between maple and ajax.googleapps (and I think one statistic service), but then most time is spend by conneting to maple and facebook connect (which fills up almost all the time).

The login does not work: I used my alternative id, which is AVt. I even requested a new password - it was sent correctly (to a different mail box, having a special character preventing much spam). And even with this pswd (just simple and and pure ASCII, no special characters, long enough) it does not work.

Time for some wheat beer ... Cheers

I looked at it at work - where it worked (layout is a matter of taste though ...)

Now at home: it needs more than 90 sec to load the login.

Then here login does not work (security settings are different, at work I do not need to care so much ...)

So what ... I do not have the patient at the moment ... seems to be not that quick for dial ups

Thx.

It needs 75 sec to to load the login.

Then (after entering my concurrent data) it tells me: "MaplePrimes has changed and we need you to update your password and profile information ..."

I will not do that for a test, may be under a different & new account

And it is a bit late here, may be tomorrow.

Will - what is the link for testing?

Would you mind do 'expand' your compact solution a bit?

It seems worth to follow it besides Maple's notation ...

Would you mind do 'expand' your compact solution a bit?

It seems worth to follow it besides Maple's notation ...

Yes, he is in Numerics / numerical Analysis. Where his project chebfun may be of interest as well,

www2.maths.ox.ac.uk/chebfun/ and www.comlab.ox.ac.uk/publications/publication2807-abstract.html

I have never looked into its details, since the project is ongoing from 2002 it can't be trivial to carry it over to Maple.

I have no doubt, that the computation can be done much faster using Maple as well. It is just, that it is very slow if one is only using the commands, which are thought to be used for that.

Yes, he is in Numerics / numerical Analysis. Where his project chebfun may be of interest as well,

www2.maths.ox.ac.uk/chebfun/ and www.comlab.ox.ac.uk/publications/publication2807-abstract.html

I have never looked into its details, since the project is ongoing from 2002 it can't be trivial to carry it over to Maple.

I have no doubt, that the computation can be done much faster using Maple as well. It is just, that it is very slow if one is only using the commands, which are thought to be used for that.

for example Nick Trefethen and references therin (no, I never used it to code s.th. in Maple):

web.comlab.ox.ac.uk/people/Nick.Trefethen/publication/publication.html

PS: as far as I remember Maple just uses a general recipe to evaluate analytic functions of matrices (so exp is just one case and it would not care for special inputs)

for example Nick Trefethen and references therin (no, I never used it to code s.th. in Maple):

web.comlab.ox.ac.uk/people/Nick.Trefethen/publication/publication.html

PS: as far as I remember Maple just uses a general recipe to evaluate analytic functions of matrices (so exp is just one case and it would not care for special inputs)

Will, certainly I should be aware that it does not make sense to ask for something substantial if it is not guaranteed that Marketing Dept is enforced to stay on St Helena for at least 6 weeks ... It is the same procedure as every year ...

In German there is a difference between "sagen" and "reden" or as we say in Bavaria "Ich sag ja nix, ich red ja bloß" indicating that nothing essential was said.