20090118, 13:19  #1 
Dec 2008
you know...around...
1101010000_{2} 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 20090118 at 13:21 
20090125, 15:53  #2 
Dec 2008
you know...around...
2^{4}·53 Posts 
Is this even interesting? A coincidence? Or is it a trivial phenomenon?
Last fiddled with by mart_r on 20090125 at 15:55 
20090125, 16:05  #3 
Nov 2008
2×3^{3}×43 Posts 

20091022, 18:14  #4 
Dec 2008
you know...around...
848_{10} 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 20091022 at 18:16 
20091024, 18:17  #5 
"Lucan"
Dec 2006
England
6474_{10} Posts 

20091024, 18:40  #6 
Dec 2008
you know...around...
2^{4}×53 Posts 

20091024, 19:04  #7 
"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 
20091024, 19:40  #8 
Dec 2008
you know...around...
1101010000_{2} 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 TEXformat?) Last fiddled with by mart_r on 20091024 at 19:41 
20091024, 20:16  #9  
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Quote:
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 20091024 at 20:30 

20091024, 20:20  #10 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 

20091025, 11:10  #11  
Dec 2008
you know...around...
350_{16} Posts 
Quote:
(z is the surface? I thought it was the room coordinate?) Maybe I'd figure it out eventually, but not today. @ MiniGeek: thanks! Last fiddled with by mart_r on 20091025 at 11:12 

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