Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
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
  A Holomorphic Function Asymptotic to Tetration JmsNxn 2 1,138 03/24/2021, 09:58 PM
Last Post: JmsNxn
  New mathematical object - hyperanalytic function arybnikov 4 6,174 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 2,195 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Should tetration be a multivalued function? marraco 17 31,653 01/14/2016, 04:24 AM
Last Post: marraco
  Introducing new special function : Lambert_t(z,r) tommy1729 2 6,992 01/10/2016, 06:14 PM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 3,598 04/21/2015, 01:02 PM
Last Post: tommy1729
  The inverse gamma function. tommy1729 3 11,921 05/13/2014, 02:18 PM
Last Post: JmsNxn
  entire function close to sexp ?? tommy1729 8 16,969 04/30/2014, 03:49 PM
Last Post: JmsNxn
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 12,127 07/17/2013, 09:46 AM
Last Post: Gottfried
  Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 5,152 06/15/2013, 08:02 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)