Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Is the following expression for tetration useful?
#7
I've been playing around a bit with that integral

.

The thing is, this integral doesn't seem to converge directly. Namely, the reciprocal gamma function blows up faster-than-exponentially toward the left. But, I found that if we make x sufficiently large, and then the lower bound not too large, it seems this gives a sort of "asymptotic" integral that gives . Take, e.g.

.

This behavior makes me wonder whehter it's not possible to somehow regularize this integral with some form of "divergent integration" technique, analogous to divergent summation for sums.
Reply


Messages In This Thread
RE: Is the following expression for tetration useful? - by mike3 - 11/10/2012, 03:19 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Is this entire expression for tetration legal JmsNxn 4 4,518 01/20/2013, 07:32 PM
Last Post: cosurgi
  Understanding Abel/Schroeder with matrix-expression Gottfried 12 13,894 05/26/2008, 08:45 PM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)