Min (f(x) / x^n) = 1/n!
My intuition suggests f(x) ~ exp(x) sqrt(x+1) / sqrt(2 pi).
Or in other notation S9^[-1] (exp(x)) ~ O( exp(x) sqrt(x) ).
More general S9^[r] (exp(x)) ~ O( C^r exp(x) x^(-r/2) ).
Also wondering about lim Gauss^[+oo](any(x)) = ?? If the limit even exists !?
I could not help noticing the resemblance to the semi-derivative of exp and S9(exp(x)). Coincidence ? Or does the semi-derivative play a role in fake function theory ?
Does for Large n,r :
a_n® a_n(-r) ~ gaussian a_n ?
( when the gaussian is good )
Regards
Tommy1729
My intuition suggests f(x) ~ exp(x) sqrt(x+1) / sqrt(2 pi).
Or in other notation S9^[-1] (exp(x)) ~ O( exp(x) sqrt(x) ).
More general S9^[r] (exp(x)) ~ O( C^r exp(x) x^(-r/2) ).
Also wondering about lim Gauss^[+oo](any(x)) = ?? If the limit even exists !?
I could not help noticing the resemblance to the semi-derivative of exp and S9(exp(x)). Coincidence ? Or does the semi-derivative play a role in fake function theory ?
Does for Large n,r :
a_n® a_n(-r) ~ gaussian a_n ?
( when the gaussian is good )
Regards
Tommy1729
