07/04/2011, 01:28 AM

(07/03/2011, 10:52 PM)bo198214 Wrote:(07/03/2011, 08:21 PM)JmsNxn Wrote:

which is totally paradoxical and seems to contradict foundations; if anyone has some light to shed on why this converges I'd love to hear it. I just want to put my name on it quick if it turns out to be anything real serious. The thread is here if you're interested: http://math.eretrandre.org/tetrationforu...hp?tid=635

Um, didnt I show in the original thread that the right side has infinite convergence radius? As well as the left side can not be equal to the right side, because the left has a singularity at 0 and the right is a powerseries development at 0.

Yes, you did show that and I do not mean to ignore your proof, but it's just no explanation for why the series still converges to over a temporary domain. If it shouldn't by all means converge, and yet it still does, doesn't that merit some sort of credit or observation?

And if you don't believe me, here's the code I'm using:

Code:

`e=2.71828182845904523536028747135266249;`

y=0.577215664901532860606512090082;

Hmn(n) = {

local(k);

k = 0;

if ((n == 0), return(0););

for (c=1, n, k += c^(-1));

return(k);

}

ln(x) = {

local(S, d);

S=0;

for(n=0,1000,

S += (x^n)*(Hmn(n)-y)/n!;

);

S = S/(e^x);

return(S);

}

Why does this converge if the two do not equal each other?

The American mathematical monthly seems very prestigious, seems like it would be hard for me to get my paper in there. And I live in Canada so I'm not sure if I could even publish there. The fibonacci one seems to be only about fibonacci numbers, and the other one I'm unsure of. I was mostly only hoping for arxiv just so that I could put a stamp on it, if you know what I mean.

But I think, that really, an exposition on semi-operators is very interesting and would have a wide appeal, so a journal could want it. I mean, as a thought experiment to the layman it's always interesting. I could write it out really simply, as well. I'm scared that it would get rejected flat out though; is there anyway I could post it somewhere where it could be edited and commented on first? I'd love to get it published in a journal but I'm sure, that very honestly, it will be hard to get it noticed.

Thanks for your help Henryk , you always seem to have an answer