Tommy's Gamma trick ?

[tommy1729]

By estimating est , we also estimated f.

We set est(1/K) = 1 + 1/k.

And we can use

A • B = f^[-1](f(A) + f(B)) to get the simpler

A * B = f(A) + f(B).

Then when we set lim n -> oo to lim N -> oo ; n = N^k , (so) we (can) compute the

CS(f(x)). [ by the estimate ]

And then exp [ Cs(f(x)) - Cs(ln(x)) ] = Cp(f(x))/ gamma(x) = g(x).

Then g(x)^{-1} = Cp(tet(x)) = (est(x) - est(x-1/k)) ~ sexp'(x)


For x > 1.

What is the desired equation.

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End of method.

It is assumed tet ' (x) = Cp( tet(x) )

1) extends beyond x E (1,2).

2) the functional equation must follow.

Also

3) we get a C^oo result

In fact

4) we get An analytic function.

All intuitively logical and we could add the functionaliteit equation to the conditions.

5) uniqueness assumed, related to 2) , 4) ofcourse .

Regards

Tommy1729