Clearly this function grows slower than any exponential but faster than any polynomial or even exp(x^t).
This implies that if our asymptotic is entire - or the function itself ?? - then it is determined by its zero's completely.
Otherwise fake function theory can be applied.
And then the fake is compl determined by its zero's.
A quick brute estimate is exp(x^T + T x^{tT}) , where T is between t and 1.
ITS not accurate i know.
All of this is ofcourse Up to a multip constant.
Regards
Tommy1729
This implies that if our asymptotic is entire - or the function itself ?? - then it is determined by its zero's completely.
Otherwise fake function theory can be applied.
And then the fake is compl determined by its zero's.
A quick brute estimate is exp(x^T + T x^{tT}) , where T is between t and 1.
ITS not accurate i know.
All of this is ofcourse Up to a multip constant.
Regards
Tommy1729
