05/12/2014, 11:35 PM
Good work guys.
Well perhaps not completely correct but I think going in a good direction.
I have the feeling that you guys are looking for Carlson's theorem.
This creates uniqueness and a newton series.
And by that we switch from the cardinality of functions to that of integers.
Afterthat we can give an integral representation of it.
Ok, maybe Im going to fast now , some more details :
Let a(x) and b(x) be entire functions that are asymptotic to exp^[0.5](x) for x > -1.
Also a(n) = b(n) for integer n.
Since a(n) and b(n) are entire and grow slower than exp , Carlsons theorem applies and
a(x) - b(x) = 0
!!!
So we can make a newton series.
And an integral representation.
And that might help in sheldon's wanted iterated algorithm ... to prove my conjecture for the coefficients.
regards
tommy1729
Well perhaps not completely correct but I think going in a good direction.
I have the feeling that you guys are looking for Carlson's theorem.
This creates uniqueness and a newton series.
And by that we switch from the cardinality of functions to that of integers.
Afterthat we can give an integral representation of it.
Ok, maybe Im going to fast now , some more details :
Let a(x) and b(x) be entire functions that are asymptotic to exp^[0.5](x) for x > -1.
Also a(n) = b(n) for integer n.
Since a(n) and b(n) are entire and grow slower than exp , Carlsons theorem applies and
a(x) - b(x) = 0
!!!
So we can make a newton series.
And an integral representation.
And that might help in sheldon's wanted iterated algorithm ... to prove my conjecture for the coefficients.
regards
tommy1729
