Could be tetration if this integral converges
(05/07/2014, 03:25 AM)mike3 Wrote: \( \beta(x) = \frac{1}{2 \pi i} \int_{\sigma - i \infty}^{\sigma + i \infty} \G(z)F(z)x^{-z}\,dx \)

Yes that should read \( dz \) My mistake ^_^

\( \beta(x) = \frac{1}{2 \pi i} \int_{\sigma - i \infty}^{\sigma + i \infty} \G(z)F(z)x^{-z}\,dz \)

As for your question on the tetration integral not working I hsould mention with \( \lambda =1 \) its no longer going to approximate tetration. I was just hoping we would still have some nice decay properties, but I guess not.
I'm really stumped on applying this to tetration at the moment. But I feel like theres got to be a way using fractional calculus, I'm just missing it.

Messages In This Thread
RE: Could be tetration if this integral converges - by JmsNxn - 05/07/2014, 03:18 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 5,790 03/03/2019, 08:55 AM
Last Post: Chenjesu
  [integral] How to integrate a fourier series ? tommy1729 1 5,856 05/04/2014, 03:19 PM
Last Post: tommy1729
  Some integral transforms related to tetration JmsNxn 0 3,948 05/02/2013, 07:54 PM
Last Post: JmsNxn
  (draft) integral idea tommy1729 0 4,677 06/25/2011, 10:17 PM
Last Post: tommy1729
  Cauchy integral also for b< e^(1/e)? bo198214 14 27,727 04/24/2009, 05:29 PM
Last Post: bo198214

Users browsing this thread: 1 Guest(s)