mersenneforum.org Mysterious connection
 Register FAQ Search Today's Posts Mark Forums Read

 2009-01-18, 13:19 #1 mart_r     Dec 2008 you know...around... 11010100002 Posts Mysterious connection Hello again, some time ago I noticed that there seems to be a strange connection between the standard normal distribution and 1/tanh(pi^2), as to be seen in A133658 in the OEIS: http://www.research.att.com/~njas/sequences/A133658 I wondered if any of you are able to tell me what's going on with these numbers. Last fiddled with by mart_r on 2009-01-18 at 13:21
 2009-01-25, 15:53 #2 mart_r     Dec 2008 you know...around... 24·53 Posts Is this even interesting? A coincidence? Or is it a trivial phenomenon? Last fiddled with by mart_r on 2009-01-25 at 15:55
2009-01-25, 16:05   #3
10metreh

Nov 2008

2×33×43 Posts

Quote:
 Originally Posted by mart_r Is this even interesting? A coincidence? Or is it a trivial phenomenon?
It's like that one where e^(pi*sqrt(163)) is nearly an integer.

 2009-10-22, 18:14 #4 mart_r     Dec 2008 you know...around... 84810 Posts News Had a look into this again today and found: 1/tanh(pi²) = 1 + 2*[e^(-2pi²)+e^(-4pi²)+e^(-6pi²)+e^(-8pi²)+...] (rather easy) A133658 __= 1 + 2*[e^(-2pi²)+e^(-8pi²)+e^(-18pi²)+e^(-32pi²)+e^(-50pi²)+...] (rather interesting) I would try to figure out why this is so, if only I could find an explanation of how the factor of 1/sqrt(2pi) in the standard normal distribution comes about... (Come think of it, this thread should probably be moved to Math or MiscMath) Last fiddled with by mart_r on 2009-10-22 at 18:16
2009-10-24, 18:17   #5
davieddy

"Lucan"
Dec 2006
England

647410 Posts

Quote:
 Originally Posted by mart_r I would try to figure out why this is so, if only I could find an explanation of how the factor of 1/sqrt(2pi) in the standard normal distribution comes about...
Are you familiar with the neat trick to find the area under the whole
curve e^(-ax^2)?

2009-10-24, 18:40   #6
mart_r

Dec 2008
you know...around...

24×53 Posts

Quote:
 Originally Posted by davieddy Are you familiar with the neat trick to find the area under the whole curve e^(-ax^2)?
Nope. Not yet.

 2009-10-24, 19:04 #7 davieddy     "Lucan" Dec 2006 England 2×3×13×83 Posts Hint: Find the volume under the surface e^-a(x^2 + y^2) Don't spoil the fun by googling
 2009-10-24, 19:40 #8 mart_r     Dec 2008 you know...around... 11010100002 Posts Assuming a sphere (which I guess is the wrong way, right?), e^(-3a(x²+y²)/2)/6pi^(3/2) (is there something like an instruction for use of the TEX-format?) Last fiddled with by mart_r on 2009-10-24 at 19:41
2009-10-24, 20:16   #9
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 Originally Posted by davieddy Hint: Find the volume under the surface e^-a(x^2 + y^2) Don't spoil the fun by googling
I am also frustrated by my inability to script maths
as I do on paper.

z = e^-a(x^2 + y^2) is the surface
Find the the volume between it and the whole plane z=0.

PS Pythagoras comes in handy.

Last fiddled with by davieddy on 2009-10-24 at 20:30

 2009-10-24, 20:20 #10 TimSorbet Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 11×389 Posts
2009-10-25, 11:10   #11
mart_r

Dec 2008
you know...around...

35016 Posts

Quote:
 Originally Posted by davieddy z = e^-a(x^2 + y^2) is the surface Find the the volume between it and the whole plane z=0.
Okay, I admit that I lack some experience in this area of mathematics.
(z is the surface? I thought it was the room coordinate?)

Maybe I'd figure it out eventually, but not today.

@ Mini-Geek: thanks!

Last fiddled with by mart_r on 2009-10-25 at 11:12

 Similar Threads Thread Thread Starter Forum Replies Last Post fivemack Hardware 7 2016-07-12 10:42 mdettweiler Linux 4 2010-03-24 04:14 MS63 Hardware 10 2005-12-03 23:38 GP2 Completed Missions 5 2004-08-12 00:34 GP2 Completed Missions 21 2003-10-24 20:02

All times are UTC. The time now is 04:21.

Sat Jan 28 04:21:55 UTC 2023 up 163 days, 1:50, 0 users, load averages: 1.25, 1.10, 1.07