## Welcome!

PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible. PlanetMath's content is created collaboratively: the main feature is the mathematics encyclopedia with entries written and reviewed by members. The entries are contributed under the terms of the Creative Commons By/Share-Alike License in order to preserve the rights of authors, readers and other content creators in a sensible way. We use LaTeX, the lingua franca of the worldwide mathematical community. On February 13th 2013, PlanetMath.org was updated to use the new software system Planetary. Some release notes are here. Please report bugs in the Planetary Bugs Forum or on Github.

## Error message

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## Latest Messages

Nov 19
I think I have a greater understanding of a tetrahedron now, your explanation was simple enough. I was thinking of studying mathematics at university, but instead opted to go into computing, repair diagnostics, <a href="http://www.compuchenna.co.uk/how-to-back-up-files/">sys backup & recovery</a> etc... which has turned out to be most helpful for me, at least.

Nov 18
Hi Planetmath, I have been doing some research on Brun's constant, and it seems the value that is converged to is 1.902160583104...Is there not a zero after the 9 ie 1.902? I saw 1.92 on the actual page that discusses Brun's constant. I just joined the site and would like to say this is one cool math site! Just wanted to check on the 1.902 vs. 1.92 Thanks, twinprime57

Nov 11
The pdf is missing on the tab, can you please reattach it? <a href="http://www.maid2clean.co.uk/domestic-cleaning/bognor-regis/">Domestic Cleaner Bognor Regis</a>

Nov 8
The last verctor w3 is incorrect it should be (1856/1129,-3132/1129,-1392/1129) get the modifications done if possible

Nov 8
my post got malformed after pressing post button

Nov 8
(1)F(x) not smaller than 0 (2)F(x) not bigger than 0 but)F(x) = (1/0) + (0*x) isn't F(x) supposed to be equal to 0 because of (1) and (2)? How could this affect modern proofs?>

Oct 25
As you can probably see, the front page of the site is a bit broken right now. I plan to fix it, and improve it a bit in the process, this weekend. There are some other long-standing bugs that need fixing as well, and I hope to get to those as I have time. I have a LOT of ideas about ways to improve the site -- as I'm sure many of you do too. The problem is that we currently have zero budget. Sincere thanks go to everyone making constructive contributions, and thanks as well for your patience. >

Oct 20
The answer should be in the Picard–Lindelöf theorem.

Oct 20
The search engine of PlanetMath is again functioning.>

Oct 11
I've done a few samples using direct summing and it seems that your: 1/(2^2q) should be 1/(2^q) Why don't you try it; I could have the formula feeding the summation wrong. ---------------- binomial(10,5)/(2^10); sum(binomial(2*k,k)*(-1/2)^k*binomial(10,k),k,0,10); (9/2)!/(5!*sqrt(pi)); ---------------------- Answers 63/256 63/256 63/256

Oct 11
Using Maxima's simplify_sum gives for a limit of 2*n ---- $\sum_{p=0}^{2n}\left(\frac{-1}{2}\right)^{p}\binom{2n}{p}\binom{2p}{p}$ $\frac{\left(\frac{2*n-1}{2}\right)!}{\sqrt{(\pi)}\cdot n!}$ Which seems strange until you evaluate -- $\left(\frac{\left(2\cdot4-1\right)}{2}\right)!=\left(\frac{105}{16}\right)\cdot\sqrt{\pi}$ So the sqrt(pi)'s cancel. Remember $\Gamma\left(\frac{1}{2}\right)=\sqrt{\pi}$ And for odd n $\sum_{p=0}^{2n+1}\left(\frac{-1}{2}\right)^{p}\binom{2n+1}{p}\binom{2p}{p}$ 0 ---------------------- Maxima also has the Zeilberger algorithm. I will copy the answer here when I understand it. If you feel you need it. -------------------- Incidently simplify_sum doesn't give a proof certificate but Zeilberger does. ---- Ray

Oct 10
Would anybody be interested in discussing a presentation here on using Pascal/Shift matrices to directly generate various Polynomial sequences via. their generating functions expressed in matrices? The underlying idea is that most generating functions are still true when indexing variables (t) are replaced with full rank singular matrices (i.e. n-1). In particular the Pascal or Shift matrices. This leads to the generating function expressed in terms of matrices and most familiar generating functions directly stating the polynomials. Also that the series is truncated automatically and exactly. I do have some theorems rather than just words :) I have a "blog" where I have stuffed some notes and results. Ray>

Oct 4
Attention Dr. Puzio: Kindly see my request to Administration. Would be glad if you would kindly do the needful.

Sep 30
This is to remind administration about my request to either a) enable " copy and paste operation" on the templates reserved for articles and messages or b) open a page on facebook which will automtically enable copying and pasting as well as uploading snapshots of articles and messages.