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One very important formula
#1
Anybody shell know this very important formula:



where are the Bell's numbers of x-th order and . For integer x one can find them here:

http://www.research.att.com/~njas/sequences/A111672

http://www.research.att.com/~njas/sequences/A144150

http://www.research.att.com/~njas/sequences/A153277

This formula can be easily derived from regular teration, but has a long history dating from 1945 ( J. Ginsburg, Iterated exponentials, Scripta Math. 11 (1945), 340-353.)

It is notable that tetration and Bell's polynomials of n-th order have applications in quantum physics: http://arxiv.org/abs/0812.4047
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Messages In This Thread
One very important formula - by Ansus - 11/03/2010, 12:21 AM
RE: One very important formula - by mike3 - 11/03/2010, 12:35 AM
RE: One very important formula - by Ansus - 11/03/2010, 01:03 AM
RE: One very important formula - by bo198214 - 11/03/2010, 01:03 AM
RE: One very important formula - by Ansus - 11/03/2010, 02:27 AM
RE: One very important formula - by mike3 - 11/03/2010, 03:16 AM
RE: One very important formula - by Ansus - 11/03/2010, 04:21 AM
RE: One very important formula - by Daniel - 11/03/2010, 03:03 AM

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