09/05/2015, 08:16 AM
About issues 2) and 3) and in general ...
Suppose we want the correcting factors c_n for f(x).
Since a_n depends on the truncated fake Taylor polynomial of degree n ,
At best we can take ^(2/n) < as explained before >.
But there is another upperbound.
F(x)^q needs to satisfy the fundamental conditions
D^a [F(x)^q] > 0 for a E (0,1,2).
In particular a = 2.
This places An upper bound on q INDEP of n but DEP on the values and rate of descent of the a_n.
And this is the balance we look for
:
the faster a_n descends , the larger q is.
And vice versa.
There we cannot " repeat the argument " as much as we want , nor choose any m-th root we want ( or other function ).
This gives hope for proving results of type
Correcting factors ~< O ( ( ln(n) n)^gamma ).
gamma ~ 1/2 is then close to a proof of TPID 17.
I call Q = 1/q the power level of f(x).
Guess this clarifies alot.
Im not sure how this relates to sheldon's integrals , Hadamard products and zeration [ min,- algebra ] yet.
Although I have Some Ideas ...
Regards
Tommy1729
Suppose we want the correcting factors c_n for f(x).
Since a_n depends on the truncated fake Taylor polynomial of degree n ,
At best we can take ^(2/n) < as explained before >.
But there is another upperbound.
F(x)^q needs to satisfy the fundamental conditions
D^a [F(x)^q] > 0 for a E (0,1,2).
In particular a = 2.
This places An upper bound on q INDEP of n but DEP on the values and rate of descent of the a_n.
And this is the balance we look for
:
the faster a_n descends , the larger q is.
And vice versa.
There we cannot " repeat the argument " as much as we want , nor choose any m-th root we want ( or other function ).
This gives hope for proving results of type
Correcting factors ~< O ( ( ln(n) n)^gamma ).
gamma ~ 1/2 is then close to a proof of TPID 17.
I call Q = 1/q the power level of f(x).
Guess this clarifies alot.
Im not sure how this relates to sheldon's integrals , Hadamard products and zeration [ min,- algebra ] yet.
Although I have Some Ideas ...
Regards
Tommy1729
