Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Is the following expression for tetration useful?
I started with the basic question:

why does:

Differentiate and we can see it. Disregarding convergence.

The fundamental theorem I proved is the following:

We also note that:

if we think of complex iterations of the derivative are in agreement with the Riemann-Liouville differintegral where is the fixpoint.

This is the thoerem that I spent about two weeks trying to prove. It's not actually that hard but I'd prefer keeping it to myself until I write a full paper with all the things I've found using this linear operator

By example I was able to deduce:

There are many more results that I found. I'm trying to compile them and make logical sense of all the connections. Lots of very interesting things happen. I'm calling these Taylor integral representations. Hopefully I'm not the only one who sees the parallel to Taylor series.

I analyzed and doing some basic integral rearrangements and substituting for and I got the result at the top.

Also in case you thought that...

Messages In This Thread
RE: Is the following expression for tetration useful? - by JmsNxn - 11/07/2012, 10:11 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Is this entire expression for tetration legal JmsNxn 4 6,403 01/20/2013, 07:32 PM
Last Post: cosurgi
  Understanding Abel/Schroeder with matrix-expression Gottfried 12 18,259 05/26/2008, 08:45 PM
Last Post: Gottfried

Users browsing this thread: 1 Guest(s)