Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Tommy's Gamma trick ?
#1
Here I Will explain the Gamma trick.

Tet(x) is computed from interpolating 1/tet(x).

So we need An interpolation for 1/tet(x).

Let Cs be the continuum Sum.

1/tet(x) = Cs ( 1/tet(x) ) - Cs ( 1/ln(tet(x)) )

Obvious.

So we need to interpolate Cs( 1/tet(x) ).

We use Cs( 1/tet(x) + ln(x) ) - Cs( ln(x) ).

Cs ln = lngamma.

Use the generalized formula < replacing product by comm operator > described below to interpolate the Cs f(x) = Cs( 1/tet(x) + ln(x) ).

Lim n -> oo

Gamma(z) = n ! n^Z / [ z (z+1) (z+2) ... (z+n)].

A Well known limit btw.

In this case the comm operator is

A • B = f^[-1](f(A) + f(B)).

So we have a limit form for the Cs(f) and therefore also

Cs(1/tet(x)).

From there we get the continuüm product Cp (1/tet(x)).
And finally Cp(tet(x)).

However to compute f(A) we need the values for tet(x).

But we know tet ' (x) = Cp(tet(x)).

We use that to set Up a recursion equation.

The details are complicated ...

Notice this is different from mike3 method for Cs and the euler formula for Cs.

Also uniqueness is not yet achieved and a few more details need to be added.

Forgive me for the incompleteness Im still considering.

Regards

Tommy1729
Reply


Messages In This Thread
Tommy's Gamma trick ? - by tommy1729 - 10/14/2015, 09:37 PM
RE: Tommy's Gamma trick ? - by tommy1729 - 10/16/2015, 12:28 PM
RE: Tommy's Gamma trick ? - by tommy1729 - 10/17/2015, 12:22 AM
RE: Tommy's Gamma trick ? - by tommy1729 - 10/22/2015, 12:34 PM
RE: Tommy's Gamma trick ? - by tommy1729 - 11/02/2015, 01:43 AM
RE: Tommy's Gamma trick ? - by tommy1729 - 11/04/2015, 12:06 AM
RE: Tommy's Gamma trick ? - by tommy1729 - 11/04/2015, 01:26 PM
RE: Tommy's Gamma trick ? - by tommy1729 - 11/07/2015, 01:02 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  semi-group homomorphism and tommy's U-tetration tommy1729 2 34 08/01/2022, 11:15 PM
Last Post: JmsNxn
  A related discussion on interpolation: factorial and gamma-function Gottfried 9 17,709 07/10/2022, 06:23 AM
Last Post: Gottfried
  " tommy quaternion " tommy1729 30 8,194 07/04/2022, 10:58 PM
Last Post: Catullus
  Tommy's Gaussian method. tommy1729 34 9,199 06/28/2022, 02:23 PM
Last Post: tommy1729
  tommy's new conjecture/theorem/idea (2022) ?? tommy1729 0 119 06/22/2022, 11:49 PM
Last Post: tommy1729
  tommy beta method tommy1729 0 595 12/09/2021, 11:48 PM
Last Post: tommy1729
  tommy's singularity theorem and connection to kneser and gaussian method tommy1729 2 1,242 09/20/2021, 04:29 AM
Last Post: JmsNxn
  Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 11,962 05/26/2021, 11:55 PM
Last Post: MphLee
  [Exercise] A deal of Uniqueness-critrion:Gamma-functionas iteration Gottfried 6 7,101 03/19/2021, 01:25 PM
Last Post: tommy1729
  tommy's simple solution ln^[n](2sinh^[n+x](z)) tommy1729 1 5,678 01/17/2017, 07:21 AM
Last Post: sheldonison



Users browsing this thread: 1 Guest(s)