Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[2014] Beyond Gamma and Barnes-G
#1
Most of you here are familiar with the Gamma function , Barnes-G function , the K-function , the double gamma function etc.

But in the spirit of my generalized distributive law / commutative assosiative hyperoperators I was wondering about

f(z+1) = f(z)^ln(z)

It makes sense afterall :

f1(z+1) = z + f1(z) leads to the triangular numbers.

f2(z+1) = z f2(z) leads to the gamma function.

f3(z+1) = f3(z)^ln(z)

Notice f_n(z) = exp^[n]( ln^[n]f_n(z) + ln^[n](z) )

So is there an integral representation for f3 ?

How does it look like ?

Analogues of Bohr-Mullerup etc ?

Hence the connection to the hyperoperators.


regards

tommy1729
Reply


Messages In This Thread
[2014] Beyond Gamma and Barnes-G - by tommy1729 - 12/28/2014, 05:04 PM
RE: [2014] Beyond Gamma and Barnes-G - by MphLee - 12/28/2014, 05:48 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Tommy's Gamma trick ? tommy1729 7 5,501 11/07/2015, 01:02 PM
Last Post: tommy1729
  [2014] Representations by 2sinh^[0.5] tommy1729 1 2,111 11/16/2014, 07:40 PM
Last Post: tommy1729
  [2014] Uniqueness of periodic superfunction tommy1729 0 1,730 11/09/2014, 10:20 PM
Last Post: tommy1729
  [2014] The angle fractal. tommy1729 1 1,996 10/19/2014, 03:15 PM
Last Post: tommy1729
  [2014] " statistical dynamics " tommy1729 0 1,537 08/31/2014, 11:53 PM
Last Post: tommy1729
  [2014] exp^[s](z) = z tommy1729 0 1,409 08/26/2014, 07:45 PM
Last Post: tommy1729
  [2014] composition of 3 functions. tommy1729 0 1,605 08/25/2014, 12:08 AM
Last Post: tommy1729
  [2014] combining some recent ideas. tommy1729 0 1,509 08/19/2014, 12:25 PM
Last Post: tommy1729
  [2014] Inconsistant equation ? tommy1729 0 1,605 07/27/2014, 02:38 PM
Last Post: tommy1729
  [2014] f(z) = f(exp(z)) = f(exp^[m](z)) tommy1729 0 1,253 07/23/2014, 11:20 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)