## New Articles

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*Ref*]**Numerical verification of the Goldbach conjecture**by Paulo FernandeskySep 28[

*Ref*]**example of contractive sequence**by pahioSep 20[

*Ref*]**contractive sequence**by pahioAug 29[

*Ref*]**Some formulas of partnership**by burgessAug 26[

*Rec*]**Kenosymplirostic numbers**by imaginary.iAug 14[

*Edu*]**How to find whether a given number is prime or not...**by burgessAug 12[

*Edu*]**BODMAS Rule application**by burgessAug 8[

*Edu*]**Tests of Divisibility- Simple tricks**by burgessAug 7[

*Res*]**0/0 is possible and has an answer**by imaginary.iAug 2[

*Ref*]**Sophomore's dream**by pahioJul 9[

*Res*]**examples of growth of perturbations in chemical or...**by rspuzioMay 24[

*Ref*]**proof of Stirling's approximation**by rspuzioMay 8[

*Res*]**Example of stochastic matrix of mapping**by rspuzioApr 23[

*Res*]**6. Discussion**by rspuzioApr 20## Latest Messages

Nov 19

Nov 18

Nov 11

Nov 8

Nov 8

Nov 8

Oct 25

Oct 20

Oct 20

Oct 11

Oct 11

Oct 10

Oct 4

Sep 30

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.

## Latest Messages

Nov 19

Nov 18

Nov 11

Nov 8

Nov 8

Nov 8

Oct 25

Oct 20

Oct 20

Oct 11

Oct 11

Oct 10

Oct 4

Sep 30

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.