help on writing a paper. JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 07/03/2011, 08:21 PM I was wondering if anyone had any suggestions or guidelines about writing a paper? I've read a few papers and I think I get the gist of how it's done. And what programs would you use? I'm assuming there's some sort of word processor that generates LaTeX? The things I'm interested in writing a paper on are semi-operators, given quickly by: $a\,\,\bigtriangle_\sigma^f\,\,b = \exp_f^{\circ \sigma}(\exp_f^{\circ -\sigma}(a) + h_b(\sigma))\\\\ [tex]h_b(\sigma)=\left{\begin{array}{c l} \exp_f^{\circ -\sigma}(b) & \sigma \le 1\\ \exp_f^{\circ -1}(b) & \sigma \in [1,2] \end{array}\right.$ which is analytic at fixpoints of f, yada yada, the thread is here http://math.eretrandre.org/tetrationforu...653&page=1 and I'm also interested in writing a short paper on this converging series(${[4,5] \le x \le [900, 950]}$): $e^x \cdot \ln(x) = \sum_{n=0}^{\infty}\frac{x^n}{n!}\psi_0(n+1)$ 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 I was also wondering if anybody could "sponsor" me on arxiv? so that I may actually e-print my paper somewhere where it counts. Is it alright that I'm not in university and I want to publish something? Am I being too rash by asking to be sponsored? I know these things are rather short. I was wondering if that's a bad thing? These papers will probably only come out to two or three pages each. Though, I think really, the shortest papers are the best. Thanks, I appreciate you taking the time to read this and thanks again for any help you have to offer. bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 07/03/2011, 10:52 PM (07/03/2011, 08:21 PM)JmsNxn Wrote: $e^x \cdot \ln(x) = \sum_{n=0}^{\infty}\frac{x^n}{n!}\psi_0(n+1)$ 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. Regarding writing articles: Well, writing papers is a hard business, as long as you want it accepted by peer reviewed journals. Though one could start with student-level journals like mathematical gazette, fibonacci quarterly, or American mathematical monthly. The arxiv on the other hand is not peer-reviewed, so the credibility of articles there is only slightly higher than you would publish it on your home page. As to the specific question: I am not an endorser on arxiv, so can not help you in this matter. JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 07/04/2011, 01:28 AM (07/03/2011, 10:52 PM)bo198214 Wrote: (07/03/2011, 08:21 PM)JmsNxn Wrote: $e^x \cdot \ln(x) = \sum_{n=0}^{\infty}\frac{x^n}{n!}\psi_0(n+1)$ 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 $e^x \cdot \ln(x)$ 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 mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 07/04/2011, 04:16 AM (This post was last modified: 07/04/2011, 08:25 AM by mike3.) (07/04/2011, 01:28 AM)JmsNxn Wrote: 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 $e^x \cdot \ln(x)$ 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? I posted a new message in the original thread. The series does not converge to $e^x \ln(x)$, but a function that is asymptotic to it for large $x$. I.e. the resemblance between the two is only an approximation, not an equality. http://math.eretrandre.org/tetrationforu...86#pid6086 « Next Oldest | Next Newest »