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


Possibly Related Threads…
Thread Author Replies Views Last Post
  Anyone have any ideas on how to generate this function? JmsNxn 3 580 05/21/2023, 03:30 PM
Last Post: Ember Edison
  [MSE] Mick's function Caleb 1 404 03/08/2023, 02:33 AM
Last Post: Caleb
  [special] binary partition zeta function tommy1729 1 334 02/27/2023, 01:23 PM
Last Post: tommy1729
  [NT] Extending a Jacobi function using Riemann Surfaces JmsNxn 2 551 02/26/2023, 08:22 PM
Last Post: tommy1729
  toy zeta function tommy1729 0 302 01/20/2023, 11:02 PM
Last Post: tommy1729
  geometric function theory ideas tommy1729 0 359 12/31/2022, 12:19 AM
Last Post: tommy1729
  Iterated function convergence Daniel 1 550 12/18/2022, 01:40 AM
Last Post: JmsNxn
  Fibonacci as iteration of fractional linear function bo198214 48 11,073 09/14/2022, 08:05 AM
Last Post: Gottfried
  Constructing an analytic repelling Abel function JmsNxn 0 640 07/11/2022, 10:30 PM
Last Post: JmsNxn
  A Holomorphic Function Asymptotic to Tetration JmsNxn 2 2,574 03/24/2021, 09:58 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)