Degamma function
#1
Dear Experts!

If we check the limits of the ratio of the gamma function and the 3rd and 4th hyperoperators (exponentiation and tetration), then we see the the gamma function should be an interoperator. I show it:
lim exp(h) / h! = 0
lim h! / h^^2 = 0
lim h!^(1/h) / h = 1/e
lim log(h!)/log(h) / h = 1
h->+oo
I guess the level of iteration of an analytic increasing function, operator depends on its limits at infinity as also its asymptote at infinity. It is important to investigate the higher- and interhyperoperators. Now, I would like to generate the functional inverse of the gamma.
I have used matrices Carleman.

Code:
Dfac(x,N,h)=intnum(t=0,h,t^x/exp(t)*log(t)^N)
/*Nth derivative of function gamma*/
n=11
A=matrix(n,n,i,j,Dfac(0.0,j,1000.0)^i/j!)
defac(x)=sum(k=0,n,(A^-1)[1,k]*x^k)

I checked if defac(24)=4, but no, it does not work.
Please, help me.

Best regards,
Xorter Unizo
Xorter Unizo
Reply


Messages In This Thread
Degamma function - by Xorter - 10/22/2018, 11:29 AM

Possibly Related Threads…
Thread Author Replies Views Last Post
  toy zeta function tommy1729 0 53 01/20/2023, 11:02 PM
Last Post: tommy1729
  geometric function theory ideas tommy1729 0 85 12/31/2022, 12:19 AM
Last Post: tommy1729
  Iterated function convergence Daniel 1 179 12/18/2022, 01:40 AM
Last Post: JmsNxn
  Fibonacci as iteration of fractional linear function bo198214 48 5,178 09/14/2022, 08:05 AM
Last Post: Gottfried
  Constructing an analytic repelling Abel function JmsNxn 0 396 07/11/2022, 10:30 PM
Last Post: JmsNxn
  A related discussion on interpolation: factorial and gamma-function Gottfried 9 19,057 07/10/2022, 06:23 AM
Last Post: Gottfried
  A Holomorphic Function Asymptotic to Tetration JmsNxn 2 2,181 03/24/2021, 09:58 PM
Last Post: JmsNxn
  New mathematical object - hyperanalytic function arybnikov 4 8,171 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 2,809 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Should tetration be a multivalued function? marraco 17 36,460 01/14/2016, 04:24 AM
Last Post: marraco



Users browsing this thread: 1 Guest(s)